Oral History Transcript — Dr. John Clarke Slater
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Interview with Dr. John Clarke Slater
By Thomas S. Kuhn
October 8, 1963
John Clarke Slater; October 8, 1963
ABSTRACT: This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with circa 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: George D. Birkhoff, Niels Henrik David Bohr, Percy Williams Bridgman, Julian Lowell Coolidge, Ebenezer Cunningham, Charles Galton Darwin, Paul Adrien Maurice Dirac, Ralph Fowler, P. Franklin, Werner Heisenberg, Friedrich Hund, Egil Hylleraas, Edwin Crawford Kemble, Hendrik Anthony Kramers, Alfred Landť, Robert Sanderson Mulliken, Norton, Wolfgang Pauli, Linus Pauling, George Washington Pierce, Erwin SchrŲdinger, Arnold Sommerfeld, M. Vallarta, John Hasbrouck Van Vleck, Norbert Wiener; Harvard University, Harvard University Physics Conferences, Kbe?havns Universitet, Massachusetts Institute of Technology, Universitšt Leipzig, University of Cambridge, and University of Rochester.
Session I | Session II
Kuhn:I raised with you before the question about attitudes toward the photon. One important piece of the answer to this is very clear in what was done to your idea in taking the photon out of it. But I wonder whether there were other signs of the same thing, whether other people had the sort of experience you had? I wonder again—and itís not unrelated, but it probably goes unrelated as it worked out—whether anything had been heard of de Broglieís thesis while you were at Copenhagen—this sort of thing?
Slater:Well, I can say more or less about this. Before I do, let me correct one slip that I made last time. I was stating the age at which I finished my graduate work, I gave erroneously the age at which I started. I was 19 when I started, 22 when I finished, as anybody can check up; I just made a slip on that. Now, coming to Copenhagen, after we talked the other day, I went home and looked up my old records. I was glad to find that got all ray calculations and everything starting with the ones in Cambridge before I went to Copenhagen, all dated. They are not arranged in order. I had to go through a number of big envelopes full of papers. Some day I will arrange them in order. I think it will be worthwhile to make a little account. When I get that done, what Iíve got there in my notes, in other words, I have all my calculations starting back then continuously up to the present. The whole works are dated.
Kuhn:You know itís just this sort of material that we want very much to microfilm.
Slater:Well, there might be isolated things, but this is an enormous, amount of paper. I always keep all my work. Most of it would mean nothing whatever to anybody but me, but I can interpret it. In the first, place, I looked for that memorandum of Kramers, and I have not found it. I would have expected to find it in there, Iím surprised I didnít, but I know it was a loose piece of paper. I may eventually still come across it. But I did find references to it, and the formula written down and so on in my own notes, as early as February 1924. So itís clear that by that date I had the copy. I think that dates the thing as having been given to me during January 1924. I know that Kramers gave it to me as a rather new thing far from publication but he thought it would fit in with what we had. So that will fix the date.
Kuhn:Then you really still feel quite sure—this is not said to doubt it, but just because thereís been such a prevalent impression to the contrary, that I donít want to let any chance to pin this one down go—that in fact, he had this in hand before you arrived?
Slater:In fact, he had it in hand before I arrived. Thereís no question on this, because, as I say, I had it all written down from him within a month after I arrived. I must look back at his papers, which I havenít had time to do yet, and remind myself of just the form that he had the equations in when he wrote the paper down, and I think Iíll find it essentially the same form that he gave it to me. And I'll be able to check that by finding the form that I have it written down in my own notes.
Kuhn:Itís been something of a puzzle anyway about that paper that, although the formula is published in a very brief note to Nature, and then in response to something of Gregory thereís a response to criticism—I havenít read the intervening criticismĒ-which has just a little bit more about whatís behind it, but nothing resembling the derivation or an argument. And it isnít until months later, in the fall or winter—-it may even be early in 1925 before itís actually published—-that the paper with Heisenberg comes out, which does give the derivation, of course, considerably elaborating the formula simultaneously, or at least a possible transit.
Itís obvious that Kramers must have derived it, he didnít just guess at it. He didnít tell me all about the details of how he arrived at it, but I suspect very much the way it was put in the later thing with Heisenberg. Heisenberg, of course, had not arrived on the scene then. He came later that spring, he came shortly before I left. So I suspect Kramers just had this sitting in his notebook, and hadnít had time to get very much further with it. Probably when Heisenberg came along they started to work on it and put it in shape.
But I also was interested to look back and find the various stages that this letter to Nature of mine went through. I can put my finger on two or three different versions that I had before the final one. I found that the final one actually was in my own typing. I had written it down. I told you that it was essentially written by Bohr and Kramers, which, I think, was essentially the case, but I had physically typed the stuff down, and probably had put the words together. But I had done this by successive toning down of original memoranda which were much. more definite about photons, etc.
Kuhn:Can I possibly persuade you to let us take those successive drafts, or do you have a photocopy here?
Slater:It would be much easier for me simply to do something. Whether itís worthwhile photocopying, or whether I should simply make out a typed copy, which I will guarantee fits the facts, I donít know.
Kuhn:You do as you please. But, in general, it's probably really easier to photocopy, and over the long pull, I think people will be happier working from photo-copy, or a Xerox copy.
Slater:We have a photocopier right here in the office. I can bring those in and have the secretary...
Kuhn:This whole line of development, I neednít tell you, whether it turned out in the form in which it was published to be right or wrong, was nevertheless immensely fruitful—
Slater:itís an interesting development.
Kuhn:and anything we can get on succesive drafts of the letter to Nature, parts of the article, or something that will represent the wrestling with this problem, or the wrestling of the personalities involved, would be extremely helpful and quite an important sort of material to preserve.
I found the following things about the letter to Nature. The first was before I went to Copenhagen. This was not a letter to Nature, this was a memorandum about that business of the Poynting vector which I was interested about with Cunningham. Most of that memorandum, which apparently I must have given to Cunningham, and he must have returned to me, was about the details of electrodynamics, and doesnít carry one very far. But there was a good strong paragraph at the end about the photons. That was perfectly straightforward photons. Then I find a first draft of the letter to Nature apparently written between Christmas and New Year of 1923-24 which was just the week after I got to Copenhagen. There I had slightly toned things down.
Then thereís another version about January 10, which is a good deal more toned down, each time saying that Iím grateful to Professor Kramers for having pointed out to me how unnecessary it was to put in the photons, etc. Then finally, also in my own typing, is a copy of the final version that sent in, and also a copy of that typed by the department secretary. So that shows that I went through at least two other versions at Copenhagen, which Bohr and Kramers were not willing to use [Telephone]. As I say, I can trace through the whole history of that thing and show that there was just more and more pressure brought on me to remove the photons entirely from the picture.
The other interesting thing that I get there, is that there is absolutely nothing in my file about the long paper. In other words, that was done not one bit by me, but entirely by them. But it looks now as if the first paragraph in that, which matches the letter to Nature that was published, perhaps was what I worked out after being told that we were not going to have any photons. So that checks my recollection that that was almost entirely Bohrís and Kramersí work. Of course, we talked things over some.
I also find that I started in the calculations leading to the paper about the quantum theory of optical phenomena just as soon as the letter to Nature was sent in, at the end of January, I was working on that steadily from that point on. So thatís what I get out of that set of notes. I will try, when I get a chance, to put those things together and make a little description of what was in the notes, and give copies of these different versions, which, I think, might be interesting.
Kuhn:It would be terribly useful to have anything you could put together from your own memory, aided by these, but also the firmest sorts of copies we could get of the documents, as other people hope to work these over.
Slater:These are short things. Iíll probably type them out; also Iíll get photocopies of them.
Kuhn:Good. I wondered a little bit, to what extent, at that point, when you were first at Copenhagen, just how clear you were initially that this "banishing" of the photons was a mistake? This is after all, in principle at least, a somewhat persuasive position also, that if thereís a way we can do this without introducing light as particles, we know they have to be waves too, and so on, that this may help.
Slater:I suspect that I was not very firmly convinced one way or the other, that I went there thinking that the photons were there, that I probably ended up feeling that one could get away without them, that there was no experiment known that absolutely demanded them. So that I think probably that I didnít have my tongue too completely in my cheek when we published the papers without any photons. But I had been argued out of it rather than coming out of it by my own accord.
Kuhn:Itís fairly clear that you were a good deal less than totally convinced because you clearlyó
Slater:Oh, I jumped right back again.
Kuhn:ówere working on the ďQuantum Theory of Optical PhenomenaĒ well before there was any experimental evidence against the Bohr-Kramers end of it.
Slater:Oh yes. No, I was working on that right from the beginning, had been thinking about it even in Cambridge. Incidentally, thereís one interesting feature connected with that, and with the ideas that I came to Copenhagen with. I donít think anybody was thinking along the lines of the relation between the finite length of the wave and the uncertainty in the energies until I came along with that. In other words, one could make out a pretty good argument that that was the beginning of the uncertainty principle.
Kuhn:Thatís one of the things I particularly did want to ask about.... I thought it was a little earlier than that. And it is an idea which Bohr makes quite a lot of.
Slater:It may be. But I would want to look back in Bohrís earlier papers to see if there is anything on that. But Iím not sure that youíll find anything earlier than this. In other words, Iím not sure that this didnít set him thinking along those lines.
Kuhn:My impression about it is, though Iím very unclear that Iím right about this, that that idea, in the first instance, is not arrived at in the literature through the Fourier transform idea—though thatís clearly a very important source of it, and a very fundamental one the way itís put a little later—- but, more nearly in connection with an analysis of the measuring problem, of the measurement of things like electron collisions for determining energy levels and so on.
Slater:Of course, you realize that the uncertainty principle as such hadnít been mentioned at this point. No, I think it would be interesting to go back into Bohrís papers and see this. I just canít remember. I know that I went there with this idea, I know that Bohr immediately was pleased with it, so that he was evidently ready to go in for it, but whether any of his papers up until then had really looked along those lines or not, I wouldnít know. I know that I was thinking along these lines because I thought Bohrís transitions, etc., just didn Ďt have this feature in them. But I can Ďt be sure that he hadnít done something in the year or so before I went there that showed that he was thinking along the same direction.
Kuhn:I talked on the phone the other day with Professor Wiener. He tells me he lectured at Goettingen, I think in 1924-25, on Fourier transforms and so forth, and included some remarks about music in which he pointed out that if you specify both the length of the note and the tone, youíve got an incompatibility there on exactly the same basis.
Slater:Of course, we know that Wiener was working just about that time, and, in fact, the year that Born was here at MIT, he and Wiener were working together on these things. Incidentally, in going over my records, I also found a copy of that thing about Poissonís brackets which might be interesting to give a copy of. That doesnít seem to be dated. But Iím sure I can go back in my original notes and find out what the date was. I found a typed MS which was not dated, but thereís internal evidence that shows about when it was. But I surely must have written this out in onghand—-I got at this late in the evening, I was going over these records, and I didnít check up on the date. But thereís one interesting feature; ĎBorní reminded me of it. I had shown that thing to Born; he was here in town at the time. Just before I had discovered it was in the paper by Dirac. Thatís what reminded me of this.
Kuhn:Again, this would be an invaluable source for us, particularly if you can look and help to give it a date. Itís interesting anyway, but it would be a great deal more interesting if we can pin the thing down.
Slater:No, I think I can date it pretty carefully. Coming back to the question as to what people were thinking about photons then, Iím afraid I canít remember. Iím afraid that all I can do is just give this evidence of how I must have been thinking and how they must have been thinking at the time. Itís obvious that Bohr and Krers were not believing the photons at the time I arrived there, because they made me pull it out of this paper.
Kuhn:Were there colloquia there that you went to?
Slater:Not much of anything, no. There was a little. There were occasional talks, but these were mostly in Danish; I had to follow them as well as I could. So I didnít get very much of a group feeling there in Copenhagen. Entirely different from the situation in Cambridge. I wouldnít say there werenít colloquia, because there were some, but I wasnít nearly as much feeling that a lot was going on as I had been in Cambridge.
Kuhn:You donít remember what any of these discussions were about?
Slater:Iím afraid I donít remember those, no.
Kuhn:Do you know when you yourself first heard of the de Broglie work?
Slater:This, I think, was after I got back. In other words, I donít think that I heard anything about that in Copenhagen. I Ďm sure it was not a lively topic of discussion, and I donít think it was mentioned.
Kuhn:Do you suppose you heard of it at all—-many people did not—until after SchrŲdinger?
Slater:Oh, I heard of it before SchrŲdinger. No, I remember definitely having seen the papers soon after they came out, but not having read them carefully. The impression I got from maybe even just reading the Science Abstracts or something rathr than seeing the paper, ďwell, here is another man who has been talking about the parallelism between waves and particlesĒ, and I did not gather the fact that he was doing it for the mechanical particles as well as the photons. In other words, I thought hereís just some more treatment of optical properties and things of that kind. So I donít think I really gathered what it was all about until SchrŲdinger.
Kuhn:Was the Comptes Rendus a journal you ever saw or looked at, to speak of?
Slater:Not as a regular thing. I knew about it. I referred to things there, but I didnít read it regularly or anything.
Kuhn:Because actually he [de Broglie] does from, I think, 1922 on, have a series of papers beginning entirely on the photon problem without any reference to the matter problem, and these gradually—-
Slater:Iím sure I was not involved in that whole thing. So it may well have been one of those that I saw when I got the impression he was working on photons.
Kuhn:I take it that certainly the year you were in Copenhagen is one that in quantum mechanics generally is characterized in a lot of places—-Copenhagen certainly also, very much in GŲttingen-as an attempt to extend the correspondence principle. Itís the year in which not only in Kramers, but also in Born and Heisenberg, you begin to see this attempt to systematically substitute differences for differentials, or differentials for differences. Itís the beginning of the period of the unmechanischen Zwang and so on. Now I just wonder whether you remember episodes involving these, your own attitudes towards any of these attempts, other peoplest attitudes towards them?
Slater:Well, you see, I was working on this too. In other words, this thing that I mentioned with the Poissonís brackets was the outcome of work that Iíd been doing along this same period. Nothing that I did got into print, but I was just as active as anybody else, I think, in trying to look for ways of taking, essentially, the dispersion formula, which gave suggestions of replacing derivatives by differences, and working that into a broader kind of mechanics. I had not got any of Heisenbergís stuff when Heisenberg came out with it, but I was very much interested, and I thought it was just along the lines that one should pursue. As I say, this Poisson bracket paper was shortly after that and shows that I had been working quite a lot myself along that same line.
Kuhn:Do these papers that youíve been able to look at give you any notion of when you actually moved to the country and out of Copenhagen?
Slater:No, but Iím sure I could find that from correspondence. I think that someday Iíll get hold of that correspondence and check it out. I havenít got it in my possession right now, but I can (???).
Let me simply urge one thing on you. Thereís obviously a very great limit whic I have already reached in the sense in which Iím going to push you about the correspondence and so forth. Do, if you will, think about making some long-run arrangement which will assure that this stuff gets put somewhere where at least ultimately any sorting you havenít done will get done, where people will, in the long run, be able to look at it. I appreciate the problem of my saying, ďlook, let me take it off and microfilm itĒ, but thereís likely to be over the long pull quite a lot of stuff there that ought, as one gets better at doing it, be really examined in some detail.
Although I feel sure youíre right in saying that if anybody simply picked up certain of these papers at this stage of the game and looked at them they wouldnít make a thing out of them, by the time the published record of the more accessible manuscripts have been studied, then the present less accessible ones then become subjects for study also, and begin to tell you things that youíd never have seen before youíd done the other work.
Slater:Incidentally, youíd be interested to know that a communication came through from Kingís project the day after you were here urging that I keep my records and so on. No, Iím definitely planning to do this, and Iíll put things in chronological order and so on where theyíre not now so theyíll be available for this. Incidentally, I came across one thing that apparently was a memorandum to myself—never intended for publication, but itís all typed out-in 1925, about this business of the differences and derivatives and so on. So I was convinced at that time, for a variety of reasons, that we were in for a new kind of wave mechanics—not wave mechanics, but quantum mechanics—so I was determined that I was going to do as much as I could along the lines of working on it. This might be an interesting thing to put in there, in a list of papers too.
Kuhn:It very definitely would. The whole sense of the consciousness of the absolute necessity for a basic change of that sort is really terribly important. I would say, you talked last time, and I was very much interested and to a very great extent convinced by what you had to say, about your sense that really Harvard was every bit as active as the European centers you visited.
Slater:I really felt that.
Kuhn:I do have the feeling—-no invidious comparisons intended, but I am trying to find out what went on, and how people felt about this—-that perhaps alone among the Harvard group, you were the person who was simultaneously deeply convinced that a change this basic was needed. I donít, for example, get the feeling from Ted Kemble, who knew that lots was wrong, that he had any notion of a likely coming need for something as conceptually as different as quantum mechanics became. And although Van certainly would seem to have come closer to feeling this way, he was at least not actively, I think, working on the attempt to change things himself. You clearly were.
Slater:I certainly was.
Kuhn:—-and were being speculative and inventive in ways that I know no other American really who was doing this sort of thing.
Slater:Well, I think this little memorandum that I spoke of just now may be pretty good documentation for that.
Kuhn:Yes. In any case, even in its absence, and I think that clearly is quite (fortunate for us). The whole nature of the steps you take with respect to the Slater note, the Bohr-Kramers-Slater paper, and so on, does represent an attempt at reform at a level more basic than—-. Well, Van suggests in one of his papers things like small variations in the inverse square law, modifications of the quantum conditions and so on, sorts of things that are much closer to the sort of suggestion that Langmuir was making in this period. In this respect, I think, youíre closer to the Europeans, or a number of them, than you are to the Americans, If this is right, itís a sort of elaboration of this early qualification of what you said about the relation of the Harvard tradition to the European tradition. Do you have any notion of why this should be, what was it that made you this way?
I doubt if it had anything to do with Harvard or European tradition or anything else. I think it was entirely inside me. In other words, fundamental, I think that I create my own environment wherever I go. In other words, I donít need to be anywhere else, I can just sit with the papers, books, etc., and produce things without any outside stimulation; Iíve always been that way. The places where Iíve gone, on a leave of absence or something of that sort, where Iíve felt that.
I was having a good time, were simply places that left me alone. The places where I felt I was having a bad time, were places that tried to stop me. For instance, I later went to Leipzig with Heisenberg. Well, I felt I got on fine there. They left me strictly alone. I could just as well have been sitting out in the country as I was sitting there in Leipzig, but it was a convenient atmosphere. I suspect it was the same way at Harvard. The thing that Harvard did was to make us aware of where you follow what was going on. That I think Kemble did very well. And that was all I needed. But Iíve never been one for talking things over very much with people. Iíve always just worked them out myself and proceeded to put them in print when I got far enough.
Look, Iím going to entirely violate my own suggested rules at this point and really jump way ahead, because it follows out of this more general question of the nature of your scientific work as against particular pieces of it. Running through from the paper weíve just been talking about, there you have a number of papers that I will call—-and this is again not an invidiou word—-relatively speculative, that tends to Ďget out of the boxí.
Now, clearly you enjoy this sort of work, and clearly youíre good at it. There are a number of people for whom this sort of thing is anathema, it isnít science, or something of the sort. This couldnít be more wrong, but Iím very much concerned with the question of who does do this and who doesnít and in what scientific environments can it be done. I think that the last paper of yours that I would say falls in this category is one in 1928 called light quanta and wave mechanics.
Slater:Thatís just about the end of it, yes.
Kuhn:I wondered sort of two things; really had you been conscious of this sort of thing coming to an end, did you regret it, what stopped it? Supposing that I guess at least part of the answer, which was that the field didnít support it so well any more, were you at all tempted to move over into nuclear work, where again doors were rather more open?
I never had any temptation whatever to move into nuclear things. Iíve always felt that I was very much interested in what went on outside the nucleus thatís what intrigued me, and I always felt that there was a great deal still to be done, and I feel that now as much as I ever did, so I've never had that temptation. But as for stopping that particular line of speculation about 1928, I think that the reason was straightforward. I felt that the real Dirac radiation theory really answered most of those questions. Therefore, there was nothing to be done directly except to work out consequences.
I knew other people would work out consequences, and I felt it was more important at that point to go back to my earlier interest in the atoms, the molecules, etc. This does not mean that I think (???)ís questions are all answered. I think that there are a lot of things in the application of radiation theory to ordinary behavior of matter, in which even now we do not have the way to proceed. Every once in a while Iíve sat down and tried to get into that again. Iíve spent periods trying to work further into quantum electro-dynamics, into some of these infinities, things like that, and Iíve never got to anything that I want to publish. But Iím going to try itagain.
In other words, in this series of books that Iím writing, I will come to the one where Iím talking about electromagnetic properties, and so on. Iím going to try again to see just what I think is right, and what I think is not complete about the present state of the theory. But I donít feel that the present application of quantum electrodynamics to ordinary problems of dispersion and so on is even logically complete. So I havenít given these up for good.
Kuhn:Clearly the sort of work you increasingly now begin to concentrate on—-the complex atom problem, the molecular problems, which are magnificent problems and offer all sorts of challenges—-are still rather different sorts of problems than the others. Not very many people combine these two sorts to anything like the extent that youíve done. I wondered how different they felt, to what extent you were aware of these as two quite different sorts of work?
Slater:No, I donít think they affected ma as being really different. I felt one had to know the fundamental theory, and I felt one could get further with that through these speculative schemes. I felt also that I wanted to apply it because it was fundamentally the behavior of matter that interested me, so I shifted back and forth from one to the other without any feeling of discontinuity at all.
Kuhn:I notice one other thing, though I think itís out of place on this list; I donít want to lose sight of it. It seems to come in 1923-24, it ought to come between 1924-25: itís this question about the Einstein-Bose statistics, and whether or not that was something you got at all involved with or listened to in Copenhagen or whether that was picked up?
Slater:I really didnít. I donít think that that was going on in Copenhagen at all, at least it was not to my knowledge. It never was under anything that I followed very deeply. I knew about it, but I didnít do much with it.
Kuhn:At this point your life becomes, as I look at it, in terms of the things you skip back and forth between, in publication, in terms of the places you are, the things youíre doing, almost too complex to try to handle across the board chronologically. Let me sort of just raise things and see how it goes. You, I take it, have no very real feeling that the year in Europe changed your whole approach, orn your life or your attitudes, it was not a revelation in any way to you?
Slater:No, it was no revelation except in the way that I learned about how Mr. Bohrís mind worked.
Kuhn:Your attitude toward Bohr, the way his mind works, is not unique, but itís a darn rare one. I wondered whether youíd run into others who felt this way about him. I am myself aware of one—
Slater:Not particularly. No, I assumed it was a matter of general personality and so on, our personalities didnít match. I suspect that if I had gone either to GŲttingen or Munich I probably would have got along very much better.
Kuhn:When did you actually get back to Harvard, not till the fall, or were you back for the summer?
Slater:I believe I was back for the summmr; I think it was about the middle of the summer. I know that my father came over and met me, and we traveled for a coupi of weeks together and then, I believe, he went on traveling more in Europe and I went back. Yes, this was probably July or something of that sort.
Kuhn:What sort of assignments did you have when you got back to Harvard?
Slater:I donít remember the first year, but I remember the general things that I taught. I could check up and find it because Iíve still got my old lecture notes. I know that I was doing some elementary, teaching, freshman physics, but I taught severaladvanced courses while I was there. I taught electromagnetic theory of light, I taught something along the statistical mechanics line, I remember; I would have to check up to find what the others were. I didnít teach regular courses in quantum mechanics because Kemble was doing that.
Kuhn:There was no attempt made yet to broaden the curriculum?
Slater:No, there wasnít. I got then quite interested in the background of classical mechanics, or classical physics, that one needs to go into quantum physics. You see, the general idea that later turned into my Introduction to Theoretical Physics with Ned [Nathaniel] Frank I had at that time. I was thinking before I left Harvard of collaborating with Kemble on a text. In fact, if you look in Kembleís Quantum Mechanics, youíll see that originally we were thinking of collaborating there, and some of the ideas in the earlier chapters I had worked on. And at that point I moved to MIT and that didnít seem so feasible. Anyway, I was interested in tying together classsical
Slater:theoretical physics and quantum theoretical physics, and how one could arrange these. I even thought at that period that I was interested in writing books about that subject.
Your whole attitude towards writing books as a proper activity is again rather different from that of most physicists. I know. I simply felt that the books we had were so hopelessly out-of-date, or were foreign like Sommerfeldís book, that I felt there was an enormous need for American books. I found that I was writirg fairly elaborate lecture notes in the courses, that I was teaching.
I began to realize those sets of lecture notes with very little work would turn into better books than the students had available, and I realized that I did that kind of thing easily. So it just seemed to me that I ought to. And then once I came here to MIT I felt even more that I ought to: the atmosphere seemed good for it. Ever since I was 30 years old, anyway, I had just been interested in this as one activity, never as the thing that would keep me away from doing new physics, but I felt that it was necessary feature of doing physics.
Kuhn:Did you have any feeling in the Harvard program that there really ought to be more and more quantum mechanics going into it than could be handled with Kembleís course alone?
Slater:No, I donít think so. I felt that that was doing it well.
Kuhn:Iíd like to point to a few of the papers of the sorts of things you were doing, and at least ask you to talk bits about some of the papers you wrote before the coming of. matrix and the wave mechanics. Thereís one very interesting paper which is, I think, #7 on this list, the one on ďPhysically Degenerate Systems and Quantum Dynamics,Ē [Phys. Rev. 26 (1925), 4l9-430.] This is again a rather inventive and speculative paper. Do you have it there in that pile?
Slater:I think I do. Yes, Iíve got them all here.
Kuhn:This is the one in which you work out a fairly elaborate ďstrength of quantization" theory, and also—which interests me even more than that you try to shift the discontinuity to quantum forces and away from space-time discontinuity.
Slater:When I read that over—I read these all over when you sent me your questionaire—-I found I remembered that less than any of the others. I donít think it really impressed me very much. I donít see it here but Iím sure that Iíve got it. No, I really have almost no recollection of what went on in my mind in working that out.
Kuhn:This is a topic you are likely to have discussed or tried out on others. Iím particularly interested in what strikes me as now an attempt to preserve a continuity which, I think, Copenhagen would have assured you had been lost from quantum mechanics.
Slater:No, I was evidently trying to preserve this very much. Of course, I was running into just the types of paradoxes that later were related to uncertainty principle and so on. I clearly must have talked the thing over with Bridgman, Kemble and [L.A.] Turner, because theyíre all mentioned here at the end. But as I say, that particular paper I'd completely forgotten until I looked back here, and Iíve essentially completely forgotten the thoughts that went into it.
Kuhn:Almost everybody does this. As soon as the field changes, the answers to these problems, this is the thing that gets erased. I suppose, if you will pardon me, because quite mistakenly people are a little ashamed of it,and simply brush it out of memory. This brings me to whatís obviously a terribly important paper. Iím not sure, one of the things I hope you can help me with, is how important it was to other people, what role it actually played. This is your hydrogen and helium spectra paper ["Interpretation of the Hydrogen and Helium Spectra,Ē Proc. Nat. Acad. Sci., 12 (1925), 732-738] This is right smack in the middle.
Slater:This is right smack in the middle. This simply occurred to me when the spinning electron-
Kuhn:Itís really before the spinning electron—-
Slater:Itís before the spinning electron, but itís when one was working up the theory of singlets and triplets.
Kuhn:It is the thing that Goudsmit does also, at more or less the same dme, before the idea of the spinning electron is available, and itís got right basic to it this whole notion of treating hydrogen in analogy to the alkalis.
Slater:Well, of course, there was also a paper by Sommerfeld about the same time, you know, along the same lines. Thatís the one that attracted the attention in general. So thatís why I didnít carry the thing further. People immediately accepted the idea, but accepted it quoting Sommerfeldís paper, and not mine, but that didnít worry me. No, this occurred to me as one of the flashes one has, that, after all, hydrogen must be exactly like an alkali, why donít we treat it this way; and I immediately went to work and looked at all the data to see if one could do this. Within a couple of weeks or something like that I assembled what was in here and wrote it down, so it was a very quick piece of work, and it all seemed to fall in line pretty well. That was all there was to it. I remember Kemble saying that he thought this was the nicest paper l'd done; he really liked the way it worked out.
Kuhn:Am I wrong in thinking, though, that this whole approach still makes trouble without spin?
Slater:Oh sure, it made complete trouble.
Kuhn:I mean in some ways what one thinks one knows about hydrogen is now not, on this view, going to give you quite the right answers. I mean, thereís an immense plausibility that this theory, after all, was working quantitatively before, and now weíre in some trouble. Wasnít that sort of reaction also felt at the time? Clearly this is a lovely paper, but it does present problems in an area one thought of almost as closed, and I wonder what that produced?
Slater:Right. All I can remember is my reaction when the spinning electron came along, and this was a great feeling of relief. I said now we can understand these things that were just so confusing before. In other words, I immediately was happy about it.
Kuhn:You saw this first in the piece, did you?
Slater:I think so. I must have.
Kuhn:Was there resistance elsewhere to the spinning electron in this country? There certainly was in Europe.
Slater:I donít think so here. At least I didnít hear any of it.
Kuhn:Bohr, Heisenberg, Pauli were all very hard to convince. Pauli took quite some time to come over on that.
Slater:Oh, I know, and, of course, thereís a whole history of Pauli and Kronig. No, I didnít see any sign of that kind of thing. And of course, the atmosphere at Harvard then was completely the one of trying to work out complex spectra because Saunders and Russell were working together on that. And this so obviously made sense there that I think everybody dumped for it immediately, they saw what it would do, and how it cleared up everything. There was no slightest hesitation that I know of.
Kuhn:You yourself in a couple of papers nevertheless raise quite serious problems, not rejecting it in the process, but you raise, for one thing, the electrodynamic problems and —-
Slater:Well, I was just trying to see if one could make electrodynamic sense about it. This thing with the photon going around and around in circles and so on shows that I was trying to speculate as to whether one could get any further or not. But I don't think I felt them as difficulties, I think I just felt them as places where maybe one could go a little further than one had.
Kuhn:What about the problem with the relative sizes of the interactions, the fact that you get spin-spin—-?
Slater:There, I think, that we all were greatly puzzled until Heisenbergís suggestion came along about the two-electron problem. In other words, that answered that question, and I think weíd been feeling the question seriously.
Kuhn:But not in ways that led you to think that the spinning electron is the wrong idea for this?
Oh no, I donít think I felt it was the wrong idea but I felt that the spinning electron by itself wasnít the whole story, and thatís why wave mechanics was such a big help. Of course, you might be interested in my general reaction to the almost simultaneous appearance on the one hand, of the spinning electron and the possibility of doing a formally complete theory of complex atoms, and on the other hand, the wave mechanics. These came along, not quite simultaneously, but almost, the spinning electron just a little bit before the other.
I was in the midst of taking the spinning electron and trying to see what could be done about getting a really logical theory of the multiplets, etc., and thatís the way I led into this dynamical theory of complex atoms. I realized there were a lot of things about that that werenít right, but I just wanted to see to what extent can one put these together in a theory that at least would hold some water logically. Right in the middle of working on that, wave mechanics came along, and I said this is exciting, these things both are exciting. I have to decide whether Iím going to stop doing the complex atoms and start doing wave mechanics or vice versa.
And I decided at that point I was so far along with the complex atoms that Iíd better stick to that and just look at the wave mechanics in a very superficial way, which I did. In other words, it was several months after Schroedinger came along before I could really get free of the other, and start in working on wave mechanics. But I did it as fast as I could. Before that year was over I had a paper or two with wave mechanics in it. I realized that this business of the magnitude of the spin-spin interaction was one of the real problems. I didnít know how it was going to be solved, but I was already for Heisenbergís paper when it came.
Kuhn:You speak here of being interested in spin, working on it, realizing that the SchrŲdinger material was important, but not getting right to it. Now what had happened meanwhile about matrix mechanics?
Slater:Well, as I said, the matrix mechanics had been going along. I was playing with that—
Kuhn:Were you playing with that?
Well, I mentioned this paper about Poissonís brackets that I had written but not published. That was in this period inóbetween. In fact, I was spending more time thinking about that than on any of these things I wrote papers about. And when I wrote the dynamical theory of complex atoms, that, as I remember, was a period when we had matrix mechanics, but when matrix mechanics was generally formulated in terms of equations of motion rather than in Hamiltonian form.
Thatís why I put that paper in terms of equations of motion, but with the thought that once you get it in classical equations of motion, then you can immediately put it into the matrix mechanics form. I donít think that was spelled out so much in the paper, but thatĎs what was in the back of my mind.
Kuhn:How did you yourself feel, particularly in view of your own Poisson brackets work, about the relative merits of the Dirac approach and the Born-Jordan-Heisenberg, the algebraic a number approach and the matrix approach?
Slater:Well, I always liked the Heisenberg-Born approach, much better than the Dirac approach. It seemed to me more concrete and straightforward.
Kuhn:In spite of the fact that youíd invented an important aspect of the Dirac approach yourself?
Slater:Well, yes, but this was expressed entirely in terms of ĎHeisenberg foreign languageí. There was no suggestion of any different kind of notation in this paper of mine, simply a commutation rule expressed in terms of multiplications of matrices and connected with the classical Poisson brackets. No, I always have liked a simple straightforward kind of notation, rather than one which tries to cover up a lot of stuff in deceptively simple language. I still use the Born-Heisenberg notation for matrices rather than the Dirac notation, just for that reason. I think when you venture to write something down, specify what youíre summing over and so on, you know what youíre doing, and the elementary student knows what heís doing, whereas when you write things in terms of q numbers and so on, youíre so likely to forget what really goes into it.
Kuhn:Unless youíre Dirac.
Slater:Unless youíre Dirac.
Kuhn:Were others as quick to pick these things up in this country as you? Clearly not everybody was.
Slater:Clearly not everybody. I doubt if very many people were picking it up so fast.
Kuhn:You must have attended Bornís lectures here in the fall of 1925?
Slater:Thatís right, I did.
Kuhn:What sort of a group did those draw on?
Slater:Well, I didnít know MIT very well in those days, so I didnít know who was here, it was mostly the MIT group. There were a few people from Harvard who came down. As I look back now—-
Kuhn:Was that the sort of thing that drew the entire physics department every time, or did it really just draw a few?
Slater:There was a group in the physics department here that was very much interested in those things. It obviously drew them, and I didnít know them then, but I got to know them obviously when I came down here. People like Will Allis, Manuel Vallarta, Ned Frank, Norbert Wiener; and a number of others were very actively interested in those things. There probably was more real interest in some aspects of quantum mechanics at MIT than at Harvard.
Slater:Even then. In other wods, MIT was no come-down when I came here from Harvard. It had somewhat different kinds of interests but there were a good many places where MIT was ahead of Harvard.
Kuhn:How would you describe it when you said it had a somewhat different kind of interests, excluding, I take it, the obvious extent of the engineering interests?
Slater:I mean the physical department specifically. I think that MIT was a good deal more sophisticated about the methods of mathematical physics. I think they understood this much better. I did not get very good training in, for example, the special functions, and many of the sorts of applications of mathematical physics that were commonplace in the European universities. I think that MIT physics had a good deal closer relationship with European universities than Harvard did. On the other hand, you probably had a little less close relation to some aspects of quantum theory, but it was not falling behind at all.
Kuhn:Do you know who here was actually responsible for getting Born?
Slater:I donít know. But it probably is mentioned in Bornís lectures.
Kuhn:I think itís indeed the Foundation or whatever supported the trip that is mentioned; Iím not sure who the individual is who sort of said Born is the man, or this is the movement we ought to have represented.
This I donít know. But I know pretty well the people who were active around here then, and I know that they were the ones who worked up the lecture notes and so on. Unfortunately Iíve got my copy of Bornís lectures at home; Iím using it right now, so I canít look that up. As I say, Vallarta was very active in all kinds of theoretical physics here. Vannevar Bush was pushing things a lot in those days. I mentioned Will Allis and Ned Frank, Julius Stratton, but there were others who arenít here any longer.
There was a man named [P.] Heymans, a Belgian who went back to Belgium. And several others whose names I donĎt remember. IĎm not sure even that [Georges] Le Maitre was around in those days. Well, they were all very much alive to what was going on. And that made a larger, more lively group for talking these things over than, Iím sure, existed at Harvard at this time. In other words, I think if Iíd been at MIT in those days I would have talked to more people than being at Harvard. So I donít doubt that they were the ones who got Born to come over. You may not realize that they also had a succession of other foreign lecturers—-Lawrence Bragg was over, Scherrer was over,Debye was over, as I remember. They had a series of lectures. Iíd come down for those lectures, so I got to see the European physicists almost more at MIT in those days than I had in going to Europe.
Kuhn:Who do you suppose came down from Harvard for those lectures?
Slater:Well, as I remember it, Kemble came to some of them, and when Van was around, I donít doubt that he came.
Kuhn:I think Van actually had—
Slater:Van was not on hand all of this period of the latter half of the 1920ís. But I donít think there were very many others. There were probably a few graduate students; of course, weíre now in 1925-30 and there were some other very good graduate students around. I canít remember whether Ed Purcell was around then or whether he was a little later, perhaps a little later (???) a number of them and, of course, Harvard also had some very good National Research fellows. Robert Mulliken was around Harvard at that time. Robert Mulliken and I lived together, at least we had rooms adjoining each other for a couple of years.
Kuhn:Do you remember what years those were?
Slater:That was soon after 1925-26 or something like that. It was before I was married—-I was married in 1926—-so it was just about the time I came back from Europe; from then until I was married, he was around most of the time. We were having rooms next to each other in a rented place.
Kuhn:Mostly though in the period before you really started working on molecules?
Thatís right. But he sort of helped get me interested in molecules. I donít think Iíd have got interested in that as fast if it hadnít been for him. No, we saw a great deal of each other. Incidentally, (Pera Lovdeen) is getting out a memorial volume to Robert Mulliken. I wrote a four or five page little essay on Mullikenís early days for that, which will be coming out before very long. So he was very active, but in this thing Lou Turner is mentioned, Sam Allison was around, Harry Barton was around. There was quite a group of National Research fellows.
And then it was not very long after that that George Shortley was on hand. There were several people who sort of divided their time between Harvard and MIT. When I came over here I was working sort of jointly with some people—-Clarence Zener was around in these parts. There was really a good deal of activity. As I look back to find who was working on the atomic theory in the early days, a surprisingly large number of those people had actually been here, right around 1930. Thatís why they were able to take advantage of my 1919 paper so rapidly. So I canít remember which of those were here the year that Born was here, but there was quite a group here, consisting to quite an extent of these National Research fellows. It was a larger place.
Kuhn:Do you remember how people felt about the Born lectures? They are clearly for most people the first extensive look at the new quantum mechanics.
Slater:Well, I donít know how many people around were interested. Certainly I was following it very thoroughly.
Kuhn:You clearly were. Van was too.
Slater:So was Van. I think that Harvard was following it quite closely.
Kuhn:But there are a lot of first-rate places in Europe, which really sort of wait around and are not much of a —-. Another person who followed it and was doing some rather creative work with it was Brillouin in Paris. On the other hand, outside of GŲttingen in Europe, and Brillouin in Paris, thereís little done with matrices. Kramers does just a bit. Itís with Schroedinger that the whole thing picks up. I wonder to what extent there was a similar phenomenon here.
Slater:Well, as I say, I just canít remember talking this over with people very much. I was following it myself, because Iíd already started along these lines from the Kramers dispersion formula. Thatís where I got interested. Itís significant that the lectures were going on here, and that certainly Born had his good-sized audience, probably 40 or 50 people, something like that; it was not a small audience.
Kuhn:Of course, at the time of the invitation nobody could have anticipated that this was what he, in fact, would have been talking about because it didnít exist.
No, I suspect that the invitation was for the solid state line, because there was a considerable amount of interest in solid state things here at MIT. Just the fact that they had Scherrer, that they had Bragg shows that they were looking for people with that kind of interest. This probably had started through the man who was then head of the department, or had been head of the department, Professor Charles L. Norton, who was a completely non-theoretical man.
He was a practical man, interested in the construction of firebricks and thermo-conductivity and so on, but he had enough imagination to realize that one ought to be interested in the theory as well as the practical side of solids. He was an interesting old character. His two sons both went on at MIT and were still around. I never knew him very much, but he was the head of the department just before I became the head, so we had a little contact in that sort of way. While he never said anything that led me to think that heíd been at all responsible for this really quite fine group of young people working on the thing, I canít believe he was entirely outside it, he certainly was encouraging it.
Kuhn:You don Ďt remember anybody saying, ďwe ought to ask Born here to talk about—-?Ē
Slater:Oh no, I certainly was not in on the planning for getting Born here.
Kuhn:Were you aware of any discontent that he should talk about such crazy stuff when after all heíd been responsible for such solid physics?
Oh, I donít think anybody would regard this as crazy stuff. In other words, I think that the guiding spirit in much of this was Manuel Vallarta. He had always been a person who was ahead of his time; that is, heís always been interested in new developments. And I think the two other people whom he saw a great deal of were Vannevar Bush and Norbert Wiener. Of course, they were also ahead of their time. Thereís one nice little story, which might be inserted into this record: this is from Bornís period here. Born was here for six months or so, and had an apartment over in the Fenway or something like that, and when he was getting ready to go, he had a party, at which I was invited, although I was at Harvard. These various people from MIT were the others, I was the only Harvard one there, I think. Born had been out shopping.
He had bought some fine toys to take back to his grandchildren, or children, or I donít know what, I think grandchildren, including an electric train. And when I got there, there were people down on the floor trying to put the electric train together, and then trying to connect it up and make it run. Well, then, they wanted to get together and make it run, there were (Van Bush) and other great engineers all plugging the thing in, and it didn't go. All that happened was that the transformer began to smoke.
At this point it was Norbert who suggested what the problem was, namely, he said, ďis it possible that this is one of the areas of Boston that is still on DC?Ē We called up the power company, and it was. Norbert also solved the problem when he organized an expedition to go out to a garage and borrow a storage battery, hook it directly to the train instead of through the transformer, knowing that these things would run on DC or AC at the 12 volt level but not at the 120, and he made it run. I thought this was quite a tribute to Norbert, the fact that he was able to diagnose this, whereas a number of other people like Van Bush couldnít figure out what was the matter.
Kuhn:When the Schroedinger equation comes out, clearly more people now do begin to take this one up. They felt, a good deal more comfort with Schroedingerís theory, with the hydrodynamical continuum theory, so that it takes a good deal of beating people over the head to get the statistical interpretation accepted. To what extent did that same pattern play itself out over here?
Slater:I doubt if it played itself out nearly as much. Certainly with me it didnít at all, because Iíd already been thinking along the lines of the statistical theory; when Bornís suggestion of the statistical interpretation came up, why I immediately said, ďwell, of course, thatís just the line Iíve been thinking about all along.Ē I donít remember anybody who was unhappy at that.
Kuhn:I know you participate as does Van in a Physical Society symposium in which you and he both talk about the statistical interpretation.
Slater:Is that so? Iíd forgotten.
Kuhn:Yes. And, I gather from some things he said, though he wasnít very concrete about who it had been, and Iím not even sure itís on my tape with him—- driving back and forth in the car he keeps telling me things that ought to be on the tape, and we donít get back to them—-but there had been a certain amount of real need to settle this view. That there had been a good deal of sympathy here and there for the notion that, ďall right, we can handle this now with continuous functions.Ē Certainly this was a large part of SchrŲdingerís quantization.
Slater:Oh yes, Well, I just donít remember coming across that situation. Of course, I think we were all happy when—-
Kuhn:You were saying that youíd all been quite happy with SchrŲdinger.
Slater:Oh I think so, I thought everybody was happy with SchrŲdingerís methods as compared to the matrix method, because they were so much more straightforward. So ever since, Iíve always regarded the matrix things as derived things and the SchrŲdinger as being a straightforward fundamental one.
Kuhn:But you donít think that the sense of a return to a semi-classical view played any large part in this preference?
Slater:Certainly not with me. And I donít think with the people in this neighborhood.
Kuhn:What about the equivalence proofs? Was this, a source of great concern and surprise when it came—-the Eckart paper, Schroedingerís own paper on the equivalence of matrix and wave techniques?
Slater:Certainly it was no surprise to me. As I told you, I really sort of skipped Schroedingerís papers when they came out, I read the first one or two, but I didnít go to the whole thing until they were all there as a unit. Then I regarded it all as part of a unified picture.
Kuhn:Itís probably simply a waste of time for me to continue to press on paper by paper as they come out. Let me simply suggest a few things, and see whether—-. Iím myself particularly interested in reactions to the transformation theory papers, both the big Dirac paper, but also the simultaneous Jordan papers, which both give a more fundamental relation between the existing versions of quantum mechanics, and simultaneously bring statistics in at a more fundamental level. Particularly, of course, Jordan gives the appearance of deriving from statistical premises the wave equation itself. Was this an impressive, exciting performance to people here or to you?
Slater:To me, not particularly. In other words, I felt that the essentials were all in Schroedinger plus Bornís statistical interpretation. I felt the rest was window-dressing; I was not impressed. Diracís I was interested in, I realized that there were different ways of formulating the thing. Jordanís interested me much less. I already had what one needed to solve problems, I was interested in getting on with solving problems.
Kuhn:Do you think this was probably a typical attitude?
Slater:I think it probably was.
Kuhn:It seems to me it may very well have been. Iím not sure that a point was missed here—-
Slater:I think youíre probably right.
Kuhn:Diracís electron theory, of course, grows directly out of this conviction that the transformation theory has to be preserved.
Slater:Thatís right. Iím sure things were missed. Iím just trying to remember the way I felt about it at the time.
Kuhn:How about the Dirac equation itself?
Slater:For the electron, you mean? Well, there again, I didnít go into it very thoroughly at the time. I felt that it surely was the right way to do it, it certainly looked as if it was, and I sort of filled it away in my memory as something to look at at some future time when I needed to use it. I felt that for the things that I was doing at that time, the Pauli way of handling this thing was all right, that I was glad that that had been essentially verified, and I wasnít working on anything relativistic or anything where I needed to use the Dirac method, so I just didnít study it very carefully. In fact, I never really went into this thoroughly enough to understand the thing until I was writing my book on atomic structure several years ago.
Kuhn:Would somewhat the same thing be true—of its relation to your own work and, therefore, the extent to which you really studied and handled it—-of the whole radiation theory as it grew up?
Slater:No, I think I studied the radiation theory a good deal earlier.
Kuhn:I didnít really mean, did it wait as late as the book on atomic structure.
Slater:No, because, after all, I had been following that kind of thing right from these early papers in this early Bohr period. So I was interested in that. And I would have kept on the radiation thing, which you notice I dropped in 1928, if it had not been for Diracís radiation theory, which I felt was really solving the problem. And I think I was all ready for that in my own thinking. I think that thereís one of these papers, I forget which one, in which I was talking about the interaction of an oscillator with a whole set of oscillators in a sense representing the radiation field. I felt that that probably was the way to do it. That was sort of the idea which Dirac then proceeded to develop beautifully in his radiation theory. But I think that IĎd been thinking enough along that line so that I was ready for it.
Kuhn:This is also the paper—-I had hoped you would talk a bit about it—- in which you draw a very close parallel between the degeneracy problem and the feeding of energy back and forth and actual interaction with the radiation field.
I felt that there was a very close parallel there. As I say, Diracís paper came along, and that essentially made the connection. I think I also was feeling that probably, by dealing with this interaction between a single oscillator representing an atom and an infinite number of oscillators representing the radiation field, that probably one could get something like the exponential decay of the atom, so that I was all ready for the Weisskopf-Wigner papers when they came out. I was already doing essentially that kind of thing. So I was very much interested in the Dirac radiation theory right from the beginning. I didnít do anything with it because I thought essentially it had solved the problems.
You see, at that period, I was spending almost all my time on the helium problem. I worked more on that helium job than I did on anything else for the period from about 1927 to 28. There were several different approaches that I took, I felt that that was the first case that had to be worked out, and I was interested in it, not merely for the two-electron atom, but also for the interaction of two heliums because I felt this was the simplest model of an alkali halide. I was coming right back to that problem, I wanted to know the repulsion between closed shells. So that was very consciously in my mind.
Kuhn:Of course, I hadnít spotted that.
Slater:Oh no, this was the simplest model of the repulsion between closed shells. So thatís why I stuck to that.
Kuhn:I missed that entirely. Of course, it makes every sort of sense. I should have spotted it. I just hadnít seen that as a return to that -interest. What about the sort of problems created by—resolved by would be a better term—-the uncertainty principle, the Bohr-Como paper, the interpretation. In certain quarters these were great big issues. What went on in Como and then more particularly immediately after at the Solvay Congress in the way of debate, knocking of heads together, people proposing paradoxes, worrying about measurement problems?
Slater:I didnít follow much of that. The whole thing seemed to me just so obvious and so simple that I just didnít see why people were arguing about it. In other words, these were the same problems that I had been worrying my head about in 1924 and 25. It seemed to me it was all straightforward. I couldnít see why people were making such a great fuss about it.
Kuhn:Did people in this country make a great fuss about it?
Slater:No, I donít think so. I think this was almost entirely a European phenomenon. I just felt I could spend my time more usefully.
Kuhn:And you think this was fairly general among that group of American physicists who were concerned at all?
Slater:I suspect it was, yes.
Kuhn:Have those problems ever become alive around MIT or around Harvard while you were there?
Slater:I donít think so.
Kuhn:Characteristically pragmatic cast of mind?
Slater:Thatís right. No, I think that we saw what the theory indicated, it made good sense, it tied in with the finite wave trains and so on; thatís that. Why spend your time on that, why not get on with the problem?
Kuhn:So there was a certain amount of explicit rejection, I take it, of this whole more philosophical concern that until 1928-29 at least was characteristic of a number of places in Europe, When you were at Leipzig, was there still any concern there anymore?
Slater:Not at all. No, the atmosphere there in Leipzig was just as pratic as it was at Harvard.
Kuhn:What were the exciting problems for people when you were at Leipzig?
I think they were the sorts of things that I was working on. That is, I had just got my 1929 paper out. I was interested in applying that to more cases. The thing that I spent my time on in Leipzig was working out the paper on cohesion in metals which came out in 1930. That was all done in Leipzig. ďCohesion in Monovalent Metals,Ē [Phys. Rev. 35 (1930), 509-529.] I remember giving colloquium talks; the only colloquium talk I ever gave in German was on that subject. Heisenberg was very much interested in that. Bloch, as I remember it, was around either there or maybe l'd seen him just before that in Zuerich—Iíd spent a little while in Zuerich before Leipzig.
I know on that same trip I saw Bloch and he was interested in the magnetic applications. Thatís when he was getting on the ferro-magnetism job. That was the thing that I was interested enough in myself so that I would have done it if he hadnít done it. I think all these questions, just of the relation of the multiplet theory to magnetic problems and things of that kind were what were concerning all of us. So that I found that on that trip I found a great deal more to talk about to the people who were there than I had with Bohr.
In other words, I enjoyed myself at Leipzig and I didnít enjoy myself in Copenhagen. And, of course, Debye was there, and heís always a pragmatic fellow, and Hund was around, and Hund was very much interested in these things. Hund, as you know, had been at Harvard for a period, so I knew Hund. Of course, he was interested in the same business of atomic spectra and the way you handle solids, etc. So those were the active topics there.
Kuhn:You remind me, of course, that you interacted with Debye—
Slater:No, I didnít interact with Debye to any extent.
Kuhn:Let me put it this way. One of the things I particularly hope youíll talk about in just as much detail as you can still recapture, is the whole set of arguments about approaches to the molecular problem, the one-center versus the multicenter approach. Hund also speaks of the opposition between his mode of analysis of these problems and the Heitler-London method, and you, of course, rate here as one of the people who did most on occasions, really singlehanded, to bring those two views together.
Slater:Well, I certainly felt right from the beginning that they ought to be brought together. I got associated with the Heitler-London type because of the 1930 paper on solids, and the paper on molecules about the same time. I felt that the Heitler-London approach was one that should be pushed further, and it was a nice illustration of the same methods that Iíd used on atomic structure, so I spent more effort talking about that. But in the 1930's solids paper, I carried the two methods through together. I was just as friendly toward the molecular orbital as to the other one, and I followed it just as thoroughly.
Kuhn:Was this perhaps in some part because of having been at Leipzig with Hund?
Slater:No, I think this was probably partly because, after all, Iíd known Mulliken for some time, so I knew his line of thinking. And Iíd known Hund before Leipzig, so I knew his line of thinking. I followed Lennard-Jonesí work when it first came out, so that I was just as much at home with the molecular orbitals in those days as I was with the Heitler-London.
Kuhn:Also on a very closely related issue you were also somebody who insists—- and itís important to insist—-that there isnít a sharp distinction between ionic treatment on the one hand, and who constantly points that oneís got to take linear combinations of these two, and that it is a matter of convenience and approximation which may work better in which problem. At this point, of course, itís hard to realize quite what separated the people involved. I take it with Hund who never really elaborated it that there was in fact strong opposition and failures of perception between these two approaches.
Slater:I think there was.
Kuhn:Can you remember exchanges?
Slater:I donít remember exchanges, no. I donít know that I was present when any exchanges happened. But I simply read the literature, and I observed that certain people wrote entirely in one language and other people entirely in the other language. A very good illustration of one who wrote entirely in the Heitler-London was Linus Pauling. I just never could understand why Linus was so one-sided on these things. Similarly, Hund and Mulliken and Lennard-Jones seemed to be almost equally one-sided on the other; I donít think they really were, but they gave that impression. So I didnít argue with either set of people. I would agree with either one when I talked to them, but Iíd just say,"look, you boys ought to get together.Ē
Kuhn:Hund says that it is really from your papers that he finally saw, or learned to see, the sense in which both groups were doing the same thing.
Slater:This may well be. I just felt that it was so important that people should see the relations that I tried to write them down in as simple, obvious language as I could. I think that Iíd understood the relations completely from the time I was in Leipzig, because, as I say, thereís where I was working out this relationship between the two for the problem with the solids.
Kuhn:But you have no recollection now of specifics of this opposition?
Slater:Specific arguments with either one, no, I havenít.
Kuhn:How long do you feel that the opposition and polarization between these two groups lasted? You said yourself that you had written a letter which we missed in our bibliography and Iíve since pulled it out carefully to look at.
Slater:That needs to go on your list, yes.
Kuhn:Because people were not getting this point out of your paper.
Iím not sure that some of it hasnít lasted almost until now. I dont think Linus Pauling ever really changed his point of view. Linus in the last few years has made remarks to the effect that he thinks the way we handle things here in this group is the right way to do it where weíre going at things from the standpoint of setting up basis functions which are very often molecular orbital type basis functions, but I donít know how thoroughly convinced he is of this. On the other hand, Robert Mulliken, of course, in a perfectly analytical way, understands what the situation is, but I donít remember his ever having used a Heitler-London calculation or anything of that sort.
I think the people who most clearly realize the relations between the two are the ones who are now in the non-empirical theory of molecules, and who will make a calculation using a molecular orbital basis set and then proceed to formulate the Heitler-London states in terms of that, and who will then proceed to find that there are cases where you just canít even define what you mean by the Heitler-London case. I think that the use of the word ďHeitler-LondonĒ in a loose way, without thinking through what one meant by it, has been responsible for a great deal of the difficulty. People have just used analogies rather than writing down what they thought ought to be done with any given calculation. And I donít think that has thoroughly penetrated even now the people who were the most strong advocates of the Heitler-London schemes. All of the present work on molecules, the quantitative work, is using molecular orbital methods.
Now weíre being very conscious of some of the lacks of logic that come in when one tries to define the Heitler-London approach. For eample, thereís a paper by (Potony) and various people on the oxygen molecule. Theyíre just trying to work over from the molecular orbital point of view and the configuration interaction point of view into some way of defining what you mean by a Heitler-London calculation. You can hardly even define it in some of these cases.
So I think that anybody whoís thought his way clearly into the thing from a point of view of really making a non-empirical calculation understands the question quite thoroughly. I think the people who still are holding out are ones who never have thought themselves into that kind of calculation. I would say, on the whole, that maybe Linus Pauling is the most extreme of these.
Kuhn:To what extent does this polarization now, I really mean between the ones who really have not now seen it through because they approach it fundamentally mathematically, and the other group, now also is a division between physicists and chemists?
I donít think at all. I think that among the chemists there are some like Pauling—-and I guess [G.W.] Wheland still thinks along the same lines—- who never have come down to the point of really making fundamental calculations and understand just what theyíre talking about, if anything, when they talk about an exchange integral. Among the physicists, I almost think that Van is nearly in the same state. In other words, Van, I would say, was one of the worst holders out among the physicists for the standpoint of the Heitler-London exchange integral type of approach.
Now Van perfectly well understands, again, how one reconciles the two kinds of approach and so on, but I think that he feels more at home talking about an exchange integral, even if he can't quite define it, than he does talking about molecular orbitals or energy band wave functions or something of that kind. They just give you two ways of looking at something, and there are many cases where you canít even give a logical definition to the exchange integrals.
Kuhn:This subject fascinates me. Iíve looked at some of it but—-
Well, thereís a lot of the theory that still isnít worked out. You know, the other day when Van was here, I was saying that Iím sort of thinking about things in succession as I write these various volumes in my book. The last volume is going to be the one on magnetic problems. This is the hardest problem in quantum mechanics, because it brings in all of the many electron aspects. It brings in also all the interactions with the motion of atoms as a whole and things of that kind.
But I want to do a better job of thinking through the relations then than has been done so far. There are a lot of things that people here in my group have done. My young colleague George (Coster) has done a lot of thinking about the relation between the different methods. Heís shown that you can give perfectly rigorous definitions of the things that essentially are exchange integrals. People in general arenít very familiar with those things.
Kuhn:I donít quite know another case like this where two groups simultaneously do things that anybody will admit are mathematically equivalent if you push them far enough. And yet theyíre quite at cross-purposes in the things they see in each of the problems, and not even quite able to isolate and discuss at cross-purposes.
Of course, part of the trouble is that to show the mathematical equivalents is very simple in the hydrogen molecule, but you get cases of very complicated problems, and it really means calculations enormously more complicated than anybody can make. One of my students, Leonard (Mathis), took the case of 6 hydrogen atoms in a hexagonal ring. This is just about the biggest system that we felt could be treated by both methods. We carried through completely parallel treatments on both schemes and showed how they fit together and so on. Well, thatís a pretty simple problem, six electrons. To do it on anything much more complicated runs into perfectly colossal numbers of functions, enormous secular equations and things like that. Well, he had secular equations with hundreds of rows and columns.
They factored, but even so we ran into them in 30 or 40 rows and columns. This is necessary even with such a simple problem. So you donít entirely get around the thing by saying, ďin principle, you can go from one to the other.Ē You have to know which is the approximation that leads to the answer you want more simply. This is one of those cases where the oxygen molecule was a sort of classic example. Itís the one that Lennard-Jones used to convince himself that the molecular orbital scheme made sense, because there the very first approximation tells where the oxygen molecule is a triplet and therefore magnetic. Whereas you start out with anything like the Heitler-London approach, and you have to go into just an enormous interaction with different unperturbed wave functions before where you can show this same thing. This is why (Potony) even wasnít sure what you mean by a Heitler-London approach to that. Well, that isnít a very complicated problem. So these things are more difficult than they seem at first sight.
Kuhn:How early would you say the chemists really got fundamentally interested in this whole new way of doing their problems? What was the importation of quantum mechanics into chemistry like? Youíve clearly been a good deal involved with that, I donít know to what extent sort of directly and in person, but through your writing.
Slater:I think that they were interested just about as soon as the physicists were, and I think that just about the first one who got interested was Linus Pauling. I think that he did wonderful things in getting the chemists aware of quantum mechanics and what it could do. When I object to his point of view on molecular orbitals and so on that doesnít mean at all that I donít think be was a pioneer in turning the chemists in that direction.
Kuhn:That was clearly a group a good deal less equipped by training, background, and condition, to take up a field of this sort than the physicists were?
Slater:Yes I think thatís one reason why they tended to go in for things that made more approximations than the physicists did. I think this since the war has changed entirely. In other words, the present development of molecular theory has been carried on much more by chemists than by physicists, and theyíre using exactly the same kind of methods. Oneís just as rigorous as the other.
Kuhn:But it was really, you think, not until the post war period?
Slater:I think it was not until the post-war period, and I think the impetus then really was Robert Milliken and his group at Chicago. He really got people back into this. Clemens Roothaan worked up methods of actually handling the thing in a practical way. Thatís what set people going at it. That was Robert Millikenís (???). He was trained as a chemist.
Kuhn:Let me come back now to your own papers. I guess I really havenít looked at all of these obviously, so Iím going to lean very heavily on you. Iíd at least like, to the exent that you can, to have you tell me what you can, about the way one of these problems grew into another and how they related. You already made for me this very interesting point that you go at helium so hard exactly because of its relation to your own earlier work. Was that in your mind from the start when you take up the helium problem, or do you take it up first as the quantum mechanic two-electron problem?
Slater:Oh I think it was in my mind. I regarded it as both—-the electron problem, but the interaction interested me just as much.
Kuhn:In the paper we already talked about, the hydrogen helium spectrum paper, this is the first place you refer to the Pauli principle?
Slater:I think it had just come out.
Kuhn:No, I donít mean this is belated. This is also somewhat to my surprise in looking at the literature: although vastly admired, almost nobody does anything with the Pauli principle until after Schroedinger—-till after it gets related to symmetric and anti-symmetric wave forms.
Slater:Well, you see, this is not literally true, because of Hundís work on complex spectra. You see, Hundís book, I think, came out just after Schroedingerís wave mechanics, but this work was almost completely done before Schroedinger came out, and Hund was using the Pauli principle and was using many of the things that I took over into my 1929 paper in that period, so that he was very conscious of it, and I was following Hundís step in great detail so that I was very conscious of it too. This, we were working on before wave mechanics.
Kuhn:But in your own case, you think, the Pauli principle, once you had seen the paper, there was really no doubt in your mind about it—-I mean, it was simply a tool from there on?
Kuhn:What about the assumption which is basic to this paper, and which, I think, would not have been so much just taken for granted as the answer available, again which comes out of the same work of Pauliís, that doublet separation is really all relativistic? I mean, this full rejection of the notion of interaction of the core, and the full attribution of the duplicity to the electron.
Slater:This was sort of taken over from the way that Sommerfeld had been writing it up in his various editions of his book, I think. In other words, that's where I got to it. Sommerfeld did a good job of writing up some relativistic doublets, and—-
Kuhn:Though with that strange business that in order to get enough of them heís got to do this business of having a change in screening constant holding the same quantum numbers with just absolutely no physical basis whatsoever.
Slater:Well, it all seems pretty mysterious, but nevertheless this seems like a good thing to work on, that method of approach.
This is what Sommerfeld does for the X-ray spectra. Now, although heís cagey about it, it surely is not what he does for optical doublets, I mean, here one is back to magnetic interaction, perhaps with some reluctance, but in the third edition he puts in an Antrag on the Schroedinger (Rumpf) model, and he goes on from there with Lande. So that there was a real running fight in the literature at the very least as to whether this was a magnetic or relativistic problem.
You clearly are taking a quite strong position on this topic, which isnít a closed topic here, and I wondered whether this troubled you, whether it ran into criticism, whether people argued with you about it. The whole question as to when the end of the (Rumpf) model comes, and I doní t mean when itís really dead, but at least when a lot of intelligent people have swung away from it, and wanted to say, itís all relativistic plus electron duplicity even when we canít make it quite work out quantitatively. When that comes is a matter of some concern.
Slater:This, Iím afraid, I havenít any light on. As I say, I wrote that paper in a hurry. I clearly canít have felt any great question in my mind about these points, or it would have taken me longer to resolve what I thought about it. I doní t remember now what my state of mind was. About the only person I talked it over with was Kemble, and he certainly didnít argue with me about it. But thatís about as far as I can say.
Kuhn:At least so far as you recollect, the magnetic interaction theory really just, at least in your own environment and among those you talked to, was not something that you felt you had to argue with anymore; you could just go ahead and take the relativistic origin for granted?
Kuhn:That did you think of Landeís work in this period? It is thoroughly relevant to problems of this sort, and he does take a quite different point of view.
I felt that Lande's work as classifying the spectra and so on was very fine. As far as the (Rumpf) side was concerned, I have a feeling, as far as I can remember my thoughts that I probably just wanted to let the (Rumpf) be a spherically symmetrical thing as far as possible and therefore I didnít like the idea of anything magnetic coming from it. I canít quote anything that proves that I thought that way, but this would be my feeling that I probably did think along those lines.
You notice, when it came to my paper on dynamical model etc., there I was clearly using this spherically symmetric model even before wave mechanics came along. I indicated in that paper apparently that I was feeling that there was something fundamental about that, and not just an approximation. I suspect Iíd been feeling that for some time before.
Kuhn:In this period, from the coming of wave mechanics, though at the very beginning of it still, without using wave mechanics, and then very rapidly using it again, youíre involved still in quite a number of different fields. Increasingly, I think, then you swing to applications, but by no means all the same applications, I mean, beginning with your complex spectra—
Of course, that was not the beginning, by any means. In other words, I think maybe Iíd better tell you a little about the things that were concerning me during that period. Naturally I got into this through helium. You may be interested in realizing that I used two quite different approaches to helium. The first was a paper in the National Academy, and that paper was more like a polarization model of helium than anything else. I said, ďhere we have two electrons. Let one of the electrons be fixed.
Letís find the motion of the second electron in the field of the first. Letís find the energy of the whole system, treating the outer electrons as a fixed thing, but the inner one as something that can move.Ē I saw then that that would give an energy as a function of the distance of the outer electron that would have the right properties. It would polarize the inner one, youíd get polarization corrections, which were being talked about as a semi-empirical thing by a lot of people in those days.
It would reduce to the right potential as this electron approached to the nucleus. Remember this is before the self-consistent field came in. So that seemed to me like a method that could lead to something fairly sensible for the helium atom, and I carried it out—- the numerical calculations were pretty crude, I think they ought to be repeated because I think theyíd be interesting. This was actually the first paper doing a number of different things. I think itís not at all sure that that approach to a self-consistent field may not have some advantages that the Hartree approach does not have.
In fact, in 1951 or 1953 or something, I proposed a simplified self-consistent field which was much along the same lines. Suppose you know the real wave function, suppose then you assume one electron is fixed, suppose you find what the other electrons are doing in the field of that fixed electron. What is the potential that could be felt by this fixed electron, coming from the nuclei and all the other electrons? This does some things that the Hartree scheme does not do. It takes account of correlation effects, of polarization and so on. For the purposes of getting a correct one-electron picture, I think that itís better than the Hartree scheme, So I think this was the first appearance of that really. It was the method more or less used by Wigner and Seitz in treating the correlation interaction between their electrons.
You fix the electrons at one spin, thatís how the others move around inside this. Well, it also, I think, was the first appearance of what is now known as the Born-Oppenheimer approximation. I had two particles, I was keeping one fixed and letting the other one move and the equations that are written down for that are just the same ones that Born and Oppenheimer wrote down. Their paper came slightly after; the two things were independent of each other. So that this representod that approach, but it did not represent an approach in which one tries to find a wave function of the two-electron system, and find the average value of the Hamiltonian. In other words, I wasnít trying to use the variation scheme.
In the other paper, again I didnít try to use the variation scheme until just the end. I tried to build up the wave function in different parts of the configuration space, and when I was all through, I tried to compute the average Hamiltonian, and was enormously disappointed because it seemed to come out very poorly. In other words, I wasnít getting anywhere very fast, and this was just when Hyleraas came along and he did use the variation scheme so I felt that he had got further than I had, although there were a number of points in both these papers that were ahead of other writers. Of course, just about that time, Hartreeís first paper came along, and that impressed me a great deal. Hartree did it as a sort of a half-empirical approach, and I immediately wanted to know, why did this work?
So I immediately set up essentially a many-electron wave function as a product function, and tried to find what the energy of this ought to be. We didnít have determinental wave functions then, at least not for a general problem, so I tried to take these product wave functions and find diagonal and non-diagonal matrix elements of the Hamiltonian to see if I could show that the non-diagonal ones were small. And therefore it would be worth getting somewhere close to a solution. Thatís in that paper. But it at the same time brought in various integrals and things which seemed amusing, and I began to think, ďwell, there ought to be something more among these integrals that one can do something with.Ē That, I think, is what set me going on the complex spectra paper.
Kuhn:When I said complex spectra I was simply giving you the wrong paper; I was thinking of the complex atoms.
Slater:Oh, well I was thinking of the 1929 paper.
Kuhn:Yes, that clearly was the one you should have been thinking of, in view of the fact that I said ďspectraĒ instead of ďatomsĒ. I am interested, and I donít want to lose here, the transition really to helium from the complete atoms paper, which in a sense seems to me perhaps the beginning of the chain —-if there is a beginning—-but certainly fits into this developmental pattern that you here picked up with helium.
I think the point on that transition was that in the meantime Heisenbergís paper on the two-electron atom came along, and that was all you needed for helium. In other words, I saw immediately how the vector model tied in with the wave function and Its symmetry for helium, and for helium I had no complications about symmetry and anti-symmetry. Heisenberg did it all. So before I started the helium work, I was perfectly well aware that for this thing you want a symmetric function and for that you want an anti-symmetric one. ThatĎs the missing link in there, I think.
To come back to the other thing, I realize there ought to be a similar missing link in the more complicated atoms, and this was the time when Wigner and the various others were coming out with all the group theory papers, and I had had no group theory. It was as simple as that. I tried to understand their papers, and I had great trouble understanding anything at all about them. But I couldnít help feeling that there must be some way out of this. When I run into a theory that I canít understand. I have a fairly universal way of approaching it. I try to work out special cases that I can understand.
I try to work from a simple special case to a more complicated one. It was obvious that, as far as the helium was concerned, there was nothing there that one couldnít understand. The symmetry and anti-symmetry there was all done by Heisenberg and all done by Dirac, it was understood completely. So I was looking back the other day in my notes on that, when I got to looking at these things, to see how I had actually got to the spin orbitals and the determinant form of those. I got at the whole thing in about three days. I said ďIím going to proceed through hydrogen to lithium and to go on to more complicated atoms and see where I get stuck."
And so I wrote down the hydrogen—-I should say I wrote down the helium. By then, of course, I was more or less familiar with the Pauli spin matrices, so that at that point I said,Ē letís formulate this in terms of a delta function, sort of a Pauli spin-matrix thing.Ē So I set up a wave function for the helium involving the statement as to what the spins are going to be, written down in terms of delta functions. I said ďthis is all very straightforward, I can do this all right. Now letís try lithium.Ē
I wrote down lithium with its third electron and set up wave functions built up so that if you remove one electron youíve got the helium-like situation, so that the outer electrons have the kind of symmetry that they want to have in an alkali spectrum. And I put delta functions in to convert these things into functions involving spin as well as orbital functions, so then I had a case with three electrons. And I said, ďNow, whatís the chance of being able to write these things in terms of determinants involving products of the spin and an orbital?Ē And on the next page I wrote them down in terms of determinants. I said, ďdoes this work out?Ē I checked term by term, it turned into a determinant, I said, ďwell, thatís all there is to it.Ē So then—
Kuhn:What gave you this step? Using the determinntal notation is clearly the key here.
Slater:Thatís right. On the next page I was using a determinantal notation.
Kuhn:In what connection did you use determinants before. What sort of acquaintance—-clearly one knew of their existence, but—-?
I was pretty well acquainted with them. But, of course, donít forget that Dirac had used determinental notation for the case where all the spins are parallel. Years back he made big determinants of many electron wave functions. This was no new idea: the only new thing was doing it with the spin, orbitalsand have them in a case where the spins werenít all parallel. So I was on the look-out for things that could be written as determinants. All I had to do was to check the number of terms that come into a 3 X 3 determinant and see if they all checked, and they did.
Apparently according to my calculations, I was perfectly satisfied with that helium case, and the next thing I did was to formulate the general case. ďSuppose we have a determinant made out of these things, then what are the formulas for the energy?" And within about the next day I had them all worked out. And I started working out multiplets. So I had no idea until I looked this up what the order of thought was. But that was it, it was simply the lithium case that was enough to give the key to it.
Kuhn:This is terribly interesting. Itís of course just the sort of thing I want, and itís the sort of thing that does not come unless you can look back at notes.
No, I wouldnít have remembered it until I looked up these calculations to see how I actually did it. I had a feeling that it was not a long-thinking thing, but it was all half a dozen pages of calculations within a couple of days. But anyway, that led me immediately into the 1929 spectrum paper, and then just about the same time I thought of this variation business, varying the orbitals to see if one could not get Hartreeís scheme out of this. I found immediately that one could.
Then I said, ďwell, why donít you put a determinant in instead of the other?Ē, and I saw that you could write down some equations that had some of these messy integrals in it. At that point I dropped it, and of course Fock came along right after that, writing down the equations, so that that was the step that I was going through there. But, these were going along sort of—-slightly after the helium job. In other words, I was thinking about this business of the general multiplet case. Obviously when I finished the helium, I wanted to go on from there.
I had to understand how to handle things more complicated than helium. So I suspect Iíd find if I looked back in all my notes that I got into this lithium case very shortly after I finished working on the helium. It certainly was within a few months. I havenít put my papers all in order to see what I was doing the day before I started trying to do lithium—-just how I got to this. But it was all a pretty consecutive line of thought.
Kuhn:I take it that with the complex spectra paper, you really felt that this line was for the moment closed off?
Slater:Oh no, I felt that as far as atoms was concerned it was closed off, and the next thing to do was to apply it to molecules themselves.
Kuhn:Right. It was just that same step?
Slater:No, I felt that the fundamentals of the atoms were closed off, which, in fact, they were. In other words, I dropped that, and thatís where Condon and Shortley and so on moved in, doing things that Iíd obviously have done if I had stuck with it. But I felt that I needed to ďcolonizeĒ the field of molecules and solids instead of going on and working out all the details of the atoms.
Kuhn:Can you tell me something about a decision of that sort? It seems to be a perfectly natural one, yet on the other hand, pretty clearly, the point at which you left it was equally a poirt that other people could pick it up and were fascinated by it.
Sure. Well, I knew they would be picking it up and be fascinated; in fact, some of that was going on around me, because this was just about, or slightly before the period when I moved over here to MIT. If you look back, George Shortley was a National Research fellow around here at that time, and he was starting to work on some of these things. [Montgomery Hunt] Johnson and various others were also doing it.
So that while I dropped it myself, people who were working around here on the same thing were following on, and I think I probably had sort of the feeling that one does when one turns over the further details of oneís problems to students. I was looking at it from that general point of. view. I wouldn't have wanted to see the thing stop, but I realized there were some fine eager fellows working at it, and felt that this was a good thing for them to work on.
Kuhn:Now how did the molecular problem compare, what were the difficulties it presented to you? I realize that itĎs intrinsically a more complex problem, and that youĎre stopped shorter sooner.
Slater:Youíre stopped shorter sooner, but I donít think in principle; I think the principles are just the same. The complication that came up then, that doesnít come up with the atoms, was that of the non-orthogonality of the orbitals, and I think that thought that through pretty thoroughly in the cohesion of monovalent metals. I felt that was the thing that ought to come before the molecules, because it was perhaps more fundamental. You see, I was still thinking along the solid state lines.
Kuhn:But did you regard that work when you did it as preparation for an attack on molecules, or might you equally at that point have gone on with solids rather than coming back to molecules?
Slater:Well, I was pretty much on the fence. I think I was interested more in the solids than the molecules all along, and I still am. But I felt you canít understand solids without also understanding molecules. So I felt I wanted to take a crack at each of these as soon as I could, so that at least Iíd know the fundamentals. And you can see that I was thinking not merely about molecules, but molecules as constituents in solids from the papers I wrote on various ions and so on, nitrates and sulfates and so on, how one was going to handle those. Those I realized had the same properties as the molecule, as the methane, etc. but one had to understand these to get very far with the solids.
Kuhn:Were you at all tempted to get into electron theory of solids, for which you didnít have to do molecules first, and it was a terribly active field at that point?
Slater:Was it a very active field at that point? Ch, you mean the kind of thing that Sonnerfeld was doing? -
Kuhn:Yes, exactly. And there was some of it clearly going on at Leipzig.
No, I wasnít much tempted to get into that because I felt that the method I was approaching was going to go further. In other words, I felt that this complete one-electron picture was nice in its way but pretty crude. No, I was working along on this many-electron scheme until the Wigner-Seitz paper came. That again turned me in quite a different direction, and I began to see that one could get a long way with the one-electron picture, but only with the periodic potential.
In other words, the one-electron picture in the constant potential always struck me as being too far from facts to get very far. Then, of course, donít forget that there was other interest in that here at MIT. You see both Phil Morse and Ned Frank had been working with Sommerfeld. They were back here then and playing around with that kind of thing. If anybody had wanted to carry that further they would have been the ones to do it. Whereas I felt that the many-electron aspect was just almost completely being forgotten—-which it had. Those papers that I wrote then aroused very little attention.
Slater:Oh, I donít think practically read the 1930 paper for years. This was the case, or had been the case, with a very large fraction of the papers I've written. I havenít got the impression that anybody was paying any attention to them until years later they came back to me. This, of course, was not true with the 1929 paper, because that obviously got some answers in a hurry. It was not true with the Bohr-Kramers-Slater, because that had a name on it. But most of the rest of the papers that I wrote I would almost say in the whole period up to 1934, when I carried the (cellular) method further with the crystals, I felt had almost no audience at all. And I think I was right, I donít think that people were reading these papers.
Kuhn:Why do you suppose that is?
Slater:Because I think they werenít thinking along the same lines.
Kuhn:To what extent was it that your approach was different, and therefore they werenít seeing what they could do with what you were doing, to what extent was it that the problems themselves were not being handled?
I suspect both. People who were interested in solids were still thinking in terms of the 3-electron theory. They thought they had all the answers, so they just wouldnít read a paper that looked completely different from that. People who were working on molecules were either interested in Heitler-London and doing fancy group theory, or were interested in molecular orbitals and werenít interested in carrying it any further than just to find the energy of the molecular orbitals. And so on.
I think that, in other words, people were all in their little lines of approach, and what I was doing was rather out of all of these lines. So they, I donít think consciously, refused to pay attention. They just werenít attracted enough by the papers as they saw them to bother to read them, which is a most natural reaction, which is exactly the same reaction I take to things out of line of what Iím thinking about.
Kuhn:Do you think this would also have been true of Mulliken and people around him?
Slater:Not entirely, because Mulliken, after all, knew me personally. I suspect that he did—-in fact, Iím sure that he did—-read my molecule paper, and Iím sure that a certain number of people in Europe picked these right up—Bloch and Bethe and so on. They were very conscious of what I was doing. But I donít think there were many in this country who were.
Kuhn:Hund was also, of course.
Slater:Oh, Hund was surely; Hund was following things very closely. But when you ask what did people say about these things, in most cases, they said nothing because they hadnít paid any attention. This is the characteristic reaction Iíve had on most of the work Iíve done.
Kuhn:Tell me more about the role of group theory in this field. You say, and Iíve talked to a number of people this way about it, it wasnít a tool that one had already got. It was terribly hard to absorb particularly as initially developed, in its highly mathematical form, so one learned from it, I take it, part of what one might show by other techniques, and then develop the other techniques.
Slater:As far as I can make out, there must have been a few centers in Europe that were teaching courses in group theory, or at least had experts in group theory, so that the few people who started writing papers about this, Heitler and Wigner and a few others, really learned it from experts who were not interested at all in this kind of applications. All of those people were very poor at exposition, and the result was that while they understood it, there was practically nothing in their paper that would allow anybody outside their own little group to break in. Now Van, I think, did; I donít know how Van got into it.
Kuhn:I forget now, because this was one of the points on which I pressed him, and he points to a particular problem, and itís on the tape, but I now remember, at which point he felt, "now Iíve got to sit down and learn it," but this was 1930 or later. This was not right at the beginning.
Slater:Yes. You see, I didnít meet any such problems. In other words, I found that the deterininantal method would do everything I wanted it to do. And I think this is true. I think that there are none of these cases where you need group theory. And having got as far as I had without it, naturally I wasnít going to sit down and worry some more about trying to understand it. I worried a great deal in the days when these first papers were coming out. I really wanted to understand these things, and I just by golly couldnít.
Kuhn:Did you wrestle with Weylís book when it came out?
I tried some. I tried these various things, and I got nowhere. So as I say, when I started the line or argument that led me to the determinants, I did it using this technique of going from one case which I can solve to the next more complicated, and the next more complicated, to see how fast I could get there, and there was no place where I had to use group theory. I never learned group theory until about 10 years ago, and I would never have learned it then if it hadnít been that George (Coster) got it down and started talking about it here in our group, and he helped me, and I then began to see what some of itís involved in.
I use it now constantly for symmetry properties in electro-orbitals and that kind of thing, and I think I understand it quite thoroughly. But I still donít use it for the many-electron case, although George (Coster) does; he likes it better. There are a number of people around who like those methods better than the determinantal method, but who can give perfectly straightforward proofs that oneís equivalent to the other. Itís just a case of choice on that. In other words, the only problems that came up in the 1930 Ďs that demanded group theory were the spatial symmetries, the wave functions. Thatís why Robert Mulliken learned it, and I presume thatís why Van learned it.
I wasnít running into those things. I was using molecular wave functions that were simple enough so I didnít have to use them. People came along afterwards on the energy-band problems which I was doing by (cellular) method, and used group theory on that. Well, I didnít, because the symmetries that I ran into, symmetries that you get from what are now called cubic harmonics and so on, were so simple and straightforward that I thought anybody could understand those cases, and I just didnít need any further machinery.
Now one writes the same thing in terms of group theory, but I certainly donít think that I was suffering from a lack of it then. I think that I had all the tricks that I had to, even though I wasnít using it. And I felt that I was—people were writing papers using group theory, and I couldnít see they were getting any further than I was without it, so I thought this was another case where I could postpone it until I could understand it.
Kuhn:Tell me just a word about the letter to the Review, the thing you called my attention to that we had missed. In some sense I think itís fair to say—-I think you said it the other day—-there isnít anything in that letter which isnít either explicit or very close to explicit in your papers. Youíre quite careful to point to these equivalents right along. Something must have happened, or failed to happen—
Slater:Well, the thing that happened was perfectly straightforward, just what I was saying a minute ago. I had no evidence that anybody was reading the papers. I thought these were things that were important enough so that if people had not picked them out of the papers, Iíd better say them over again, hoping that this would catch peopleís attention even though the fact that it appeared in the papers didnít.
Kuhn:Was there any particular evidence of this misunderstanding that made you feel—
Slater:I just canít remember. I canít remember, except that I simply observed that the argument was still going on. Whether I may have talked to Robert Mulliken and found that he had not read the paper or what, I donít know; this could have happened, but I just donít know. I undoubtedly talked to somebody and found that he had not read that paper, and thought that he ought to know what was in it, and decided that I ought to write it down more explicitly.
Kuhn:This letter, I take it, from the fact that youíve emphasized it as something thatís got to be part of this picture, must have had an effect that the paper did not have. Was it more widely—-?
Slater:I think perhaps it was a little more widely read, but even it didnít have much effect. In other words, I had mentioned it because it sort of completes that picture. But I donít think that these things were very widely under stood.
Kuhn:Your emphasis on the length with which this misunderstanding, or source of misunderstanding continues, really does surprise me.
Slater:No, I really think that it almost still continues.
Kuhn:I find myself out of questions. I shouldnít be.
Well, I find myself just about out of remarks as a matter of fact. I think we pretty well carried things up to early 1930ís, and thatís what youíre most interested in. There were some questions you asked in your questionaire which we only barely touched on. For example, you asked how I found MIT as compared to Harvard, and Iíve said something about that. In fact, Iíve probably said almost as much as I need to, but going on to the early 1930ís—you see I came here in 1930—I felt that the group, including the ones who were already there plus the ones that we were bringing in was a good deal livelier group in these general fields than Harvard was.
Of course Tech, was building up very rapidly, but I think that the important thing is to realize that it already had a great deal before Compton came. People tend to forget that. Then we had the newly arrived people from Sommerfeldís lab, namely, Phil Morse and Ned Frank and Bill Allis had been over there, so we had that view of what was going on in Europe, which Harvard didnít have. We had, I think, a rather better preparation in mathematical physics for the students. I found that when it came to understanding mechanics and electromagnetic theory and things, that the stage of sophistication here was a good deal higher than it was at Harvard, I started almost immediately teaching a course in mechanics or mathematical physics which I worked into with Ned Frank, and immediately was beginning to learn things that I never learned before.
I never learned rigid dynamics properly. I never learned quite a variety of things that I found everybody here knew about. So that I got steered away from my intention to write a book on quantum theory by the fact that there were a lot of other things that I realized that I didnít know that I had to learn first. So, in other words, I didnít feel it was a come-down at all. I felt that it was perhaps on the whole the opposite.
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