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In footnotes or endnotes please cite AIP interviews like this:
Interview of Hans Bethe by Thomas S. Kuhn on 1964 January 17,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Part of the Archives for the History of Quantum Physics oral history collection, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family background, 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 itnerpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Niels Henrik David Bohr, Enrico Fermi, Walther Gerlach, Erwin Madelung, Linus Pauling, Erwin Schrodinger, Karl Siegel, Arnold Sommerfeld, Albrecht Unsold, Gregor Wentzel, Wilhelm Wien; and Universitat Munchen.
I would like to have you start as near to the beginning as you can with emphasis on your development of an interest in the sciences but also on the environment for this.
Well, I think the earliest I can remember is that I was interested in numbers, in arithmetic, and I used to play with numbers, finding prime numbers and making tables of squares and higher powers; I was fascinated with powers at an early age. I became fascinated with algebra as soon as I learned about it. I never was much interested in geometry and I was never very good with my hands. However, I did become interested in constructing things with a "mechano-set" and in doing some experiments, or rather I should say verifications, of statics -- pulleys and the like. This was about at the age of 13 or something like that, but the playing with numbers goes back as far as I can remember and farther. The making of tables of powers goes back to when I was maybe 10 or 11, and that stayed with me all the time.
Was there background for this in the home? Your father was not a mathematician.
No, my father was a physiologist. He knew more mathematics I think than was usual at the time for a physiologist; he knew calculus which was rare among physiologists at that time. When I was about 14 I found textbook on calculus and analytic geometry which wasn't very good but which I stole and read on the sly. I wasn't supposed to.
When you say you weren't supposed to --
Well, my parents did not like my spending so much time on these matters. They said I should play and I should play with the other boys and if I was alone and not doing school work they would much rather have me build structures with the "mechano-set" than go into mathematics. However, mathematics was the thing that most interested me and they thought this was much too difficult for me, but I did it anyway.
What was it about mathematics? It wouldn't be simply the difficulty of the mathematics that they wanted to keep you from.
It would make me one-sided and perhaps be too much of a strain on my brain, but I think it was mainly that it would make me one-sided. So anyway I learned calculus about at that time; it was a book which was called, I think, Calculus for Natural Scientists, and it was written by Schonflies who was quite well-known as a crystallographer. It was fairly good, I think; it had a lot of ex les from physical chemistry reaction rates and so on which made good sense. Then I got some mathematics in high school; I got some physics which was moderately interesting, not terribly interesting.
Where were you then? This would be gymnasium?
Yes, I was in the gymnasium in Frankfurt. I think it was a good school. I disliked the classics, which were emphasized. I was not bad in this. I always managed to get a B or so in the classics, but I had no idea why I should learn all this stuff. I think this gets me pretty well to the end of the gymnasium. I was always doing some mathematics and a little bit of physics on the side.
How far had you gotten in these subjects by the time you got through the gymnasium?
Not terribly far. In fact, at the end of high school, high school had caught up with me. We had in the last two years a special course which was elective and which only existed for about six years or so and we were fortunate in being just within those six years. We could take about 10 hours of electives and among this option were three additional hours of mathematics and two hours of physics, and this was very good. So we got quite a good grounding in calculus; I think we got about as far as the normal first year college here and by that time it was much that I had learned on the sly before; then I did not go beyond that.
How about the physics?
The physics was fair, very classical, with a very good course in mechanics of trajectories. I think we got as far as Kepler's motion. We did optics in a quite uninspired manner, lots of geometric optics, very little physical optics which was not well explained, and a tiny bit of electricity. We did not even get to alternating current circuit theory; we learned about Ohm's law and Kirchhoff's law but it was uninspired. There was nothing about atomic theory. Whatever I knew, which wasn't very much, I got from popular books and this was not really very challenging. I just barely knew that there were isotopes. I had heard that there was something like the quantum theory.
Would that be the older quantum theory?
Yes, the older quantum theory. This is now 1923 and I graduated from high school in '24 and about that time, I think about in my senior year, I heard a talk by the theoretical physicist in Frankfurt, [E.] Madelung, who tried to explain the quantum theory but who obviously didn't know it very well himself and it was not very clear whether he believed in it. I came away with the impression that he believed there was something in it but that it was something extremely vague.
Did he talk about it, do you remember, entirely in terms of the Schrodinger equation?
No, that didn't exist yet.
I'm sorry, I'm jumping two years ahead. They were still the old theories.
So it was the very old theory, Bohr's theory, and he mentioned I believe -- but about that I'm not sure because I may have heard it later -- that there were great difficulties about helium and about having to introduce half-integer quantum numbers . But it's more likely that I heard that later on when I went to the university.
Was this a lecture at the university or was this a popular lecture?
It was a lecture given at the university but a popular lecture; it was for the public. They had such popular lectures three or four times a year.
Did many people come? Was that a popular entertainment?
Oh, maybe 50 or 100. I remember going to lectures on more natural science subjects. My father used to give a lecture now and then. The natural science lectures were better attended than the physical science; there might be a hundred or two hundred people at my father's lecture and certainly less than a hundred at this quantum mechanics lecture. The city of Frankfurt had some reputation for being interested in science; some of these lectures were given by a foundation which went back to one benefactor, the (Senkenberg) lectures. There was some participation by the public. I had no idea that physics was exciting at this time. I had heard about relativity theory but didn't know what it was about; I didn't even know that it was about the velocity of light. So you might ask, why did. I go into physics.
Now at this point if somebody had asked you what you were going to do, what you were going to be, what would you have said?
I would have said "a physicist" in spite of not knowing what this was about. I knew one thing, namely, that there was something like theoretical physics, that it was possible to apply mathematics to natural phenomena. I had been interested in some of the electricity calculations even in some of the mechanics and when I went then to the university -- I went to Frankfurt. University for two years -- I took some mathematics lectures and it was really the mathematics lectures that showed me that I was not a mathematician.
Mathematics was then still an open possibility at the time you went to the university.
A completely open possibility.
Why would you have said 'a physicist' then? I expected that you were going to answer the question by saying, "I would have said I was going to be a thematician."
Yes, yes, that would have been natural. I think what later became more clear to me was already then clear. In the first term I took two courses in mathematics: one was what might be called advanced calculus and the other was number theory. The number theory was extremely good. It was quite interesting. It was much too advanced for me, but I could follow it somehow. The professor must have been quite wonderful if he made it possible for me to follow and at the same time gave quite advanced theorems. He was quite a well-known man -- [Karl L.] Siegel -- and I enjoyed it very much. I didn't work very much for it; I did the problems that he assigned but no more. I was quite sure that this was not what I wanted to do because I did not find any interest in the "l'art pour l'art"; I did not find mathematics for its own sake interesting. What I found interesting was to have mathematical tools and apply them to something that had to do with the real world. I think this had been vaguely clear to me before and became much clearer to me when I now saw what mathematics was. Now the other course, the advanced calculus, I found essentially dull. I had the reaction that I already knew how to differentiate and integrate and this was what I wanted to know; I wasn't very much interested in epsilons and deltas. It seemed easy enough to do but it didn't seem to get me any farther. So I think this indicates the state of my mind. I had a very bad lecture course in physics which I mostly cut.
Was that experimental?
Experimental physics, yes.
Yes. And I had quite a good course in chemistry. For some time I considered chemistry as a possibility, physical chemistry.
Was there any hint in the physics at this point yet of the excitement in it?
No, none whatever.
So in your first year at least, you discovered nothing about it.
I discovered, nothing. I read some textbook on physics while I was not attending the lectures, but it was old fashioned.
Do you remember what textbook it was?
It was (Lommel) and it was all right but certainly not exciting. Physics became interesting the second year. The second year I took two courses: one was advanced experimental physics which was given by [K. W.] Meissner, who was very interesting and who went into modern physics. He told us about -- no, it may not have been Meissner -- I think it was Gerlach who gave the lectures. In fact I'm pretty sure. Meissner came later to Gerlach's place. I'm sure of that. Gerlach had lots of enthusiasm and talked about atomic structure and the Bohr model and the Stern-Gerlach experiment and this was good. Then there was Madelung. I don't quite remember which of the six courses Madelung gave; you know, they have a cycle of six lectures. I know that one part of it was relativity theory, Lorentz transformation and so on, which seemed somewhat difficult but interesting. But the really interesting thing was Gerlach. Gerlach became somewhat interested in me, in the way I did the problems and he also knew my father. He told me, "Well, you shouldn't stay here; you should go to Sommerfeld."
It was clear to both of you at this point that you were not going to be an experimentalist.
Yes, this was clear. I took the laboratory work, which I did without distinction and without breaking too much. I took chemistry laboratory work which was mostly destructive of my clothes because I did most of the chemistry on my suit, so I knew I wasn't made to be an experimental chemist; I also knew--well, the physics laboratory was quite interesting. In fact, Meissner -- I think it was Meissner then --
This is something we can check. I usually know something about the curriculum, but in this case there was nothing printed between '23 and '26. Gerlach was still there in the summer semester '23, and I think --
I started the summer semester '24.
Yes, unfortunately, you see, your curriculum at Frankfurt falls right in the period when, I think because of the inflation, they stopped printing the curricula in the Berichte [Phys. Zs.]. I don't have a catalogue for Frankfurt in that period.
They should be obtainable. I know that Gerlach was still there and that I heard the first lecture course from Gerlach. Then I'm pretty sure I also had Meissner because I think Meissner told me to do a little bit of more advanced lab work in the process of which I set a small fire by means of an electric arc. Then, however, I managed to get some quite decent spectra of something or other -- I don't remember what it was. This certainly was Meissner and not Gerlach. But when I went from one to the other I really don't know. It is quite possible that it was Meissner who told me to go to Sommerfeld. Anyway, one of the two did and wrote a letter to Sommerfeld and I was very happy to listen to the advice, so in the summer semester of '26 I went to Munich.
While you were still at Frankfurt was your family now reconciled to your doing this?
Yes, my father was completely reconciled. It was quite clear once I was at the university that this is what I would do. In fact, this is what he would have recommended himself, I think, and they no longer had any worries that I would be "one-sided".
Was that because it was physics or because you had developed in other ways also?
I suppose the latter. My mother didn't like the idea that I would be a theoretical physicist simply because she thought there wasn't any living in it. She said, "Well, why don't you become an engineer?" I remember her saying this. "An engineer would have interesting work and would have red cheeks, and a theoretical physicist would always sit in his office and do calculations." But this opposition was very, very mild and my father certainly was completely in favor of it. In fact, my father was very interested and I remember these two years as very good years of relations with my father. He liked to listen to me, he liked me to tell him what I was learning in physics and he would then talk about it. Many of the things were new to him and it was a very good time.
Did you have friends who were also going through this or did you have brothers and sisters?
I had no brothers and sisters at all. I had two friends from high school, both of whom were generally interested in that direction. Very soon they decided on chemistry, but the first few courses we took together. One also had to leave Germany and is a chemist in a small firm in England. He is really the technical leader of this firm; the other never got very far. Both went into physical chemistry. One of them, namely the one who is now in England, then went to Munich with me; by that time we no longer took the same work, but we still were very good friends. I don't know whether I influenced him or he influenced me, but at any rate we both decided to go to Munich. There was nobody directly in theoretical physics in my generation who influenced me. In fact I mostly talked to these two people and then to some friends who had nothing to do with science at all.
Was there anybody, besides Madelung, lecturing in theoretical physics at all? Lande had left by that time?
Yes. Madelung's assistant was Lanczos; I think he gave some lectures, but I don't think I ever heard them and I'm not even sure that he did. If so, it was some very advanced course -- you know the German system where the professor gives the more elementary courses because they bring in more fees and the Privatdozent gives the advanced courses which don't bring in the fees.
Your real excitement then, to the extent that there was excitement about physics, really came from the experimentalists.
Yes, it was Gerlach and. Meissner and I think both about equally.
That's very interesting, I think, that that should have been the situation.
Yes. Still I knew that I was going to be a theoretical physicist.
Your second year was really '24-'25.
No, '25-'26. I started in '24-'25.
Yes. This is of course the year in which things begin to break wide open. Did you know anything about that while you were there?
The Born-Heisenberg-Jordan paper, the Schrodinger paper?
These were just not mentioned?
So all this starts for you when you get to school. Did it start right away?
It started almost right away.
You got there for the summer semester then, in '26?
Not quite right away. I went and registered for Sommerfeld's general course which was differential equations of mathematical physics, I think probably the best course he gave -- a very beautiful course but having nothing to do with the excitement in the field. I went to call on him and he said, "Well, from what Meissner wrote me, I will admit you to my seminar," so that's where Meissner came in. So I went to his seminar and this seemed quite difficult at first, but very soon -- there may have been one or two talks about something else -- but very soon the seminar was about Schodinger's papers. Schodinger's papers had not yet appeared, but they were in the proof stage.
The first one or two may already have been out.
The first may have been out, yes, but anyway the seminars discussed all these papers. Sommerfeld got the galley proofs of the papers that were going to appear and he just distributed those among the members of the seminar. Each of us had to give a talk about something. The first seminar was given by Unsold and was about the introduction by the Hamilton-Jacobi equations which made no sense to me whatever.
You'd never had dynamics at this level so that Hamilton-Jacobi equations were brand new to you.
Yes, yes. But then came the Schrodinger equation, never mind how it was obtained, and once you had the Schrodinger equation you could do things with it. All right, and then there were several talks about the hydrogen atom and so on which made perfectly good sense to me.
Physical as well as mathematical sense?
I think just mathematical sense. I knew the Bohr theory, I knew what result one ought to obtain.
When you say you knew the Bohr theory, how elaborately did you know it?
Oh, I had in the meantime read Sommerfeld's book, Atombau und Spektrallinien. This I did during my first year, I think it was, at Frankfurt.
Had you read other things of that sort?
Just the 'Bible'!
Just the 'Bible.' That it was the 'Bible' was after all quite good! So I knew the experimental facts and the old explanation. This may have been the first year or the second year, I don't know, but it probably was the second year since the first year I probably wouldn't have had enough sense to look for it and it may well have been Gerlach or Meissner who drew my attention to it.
This seminar of course interests me terribly, this first view of the Schrodinger equation, so anything you can remember about it -- do you remember who was in the seminar this summer?
I remember [Karl] Bechert and I remember Bechert had the job of coaching the students before they gave a talk. Then there was [Heinrich] Ott, 0-t-t, who also gave a lecture course. He became Professor at Würzburg. During my first year in Munich, he gave a lecture course on X-rays and crystal structure, which I found very interesting and which then had something to do with my thesis. Then there was Wentzel and he was probably the most interesting of the whole group. I had the impression, here was the man who really knew things and who probably knew more than Sommerfeld. He gave a beautiful course on dispersion theory, old-fashioned dispersion theory, which I am sure was not the first semester but the second or third. He probably talked the most in the seminar whenever there was discussion and there was lots of discussion.
Were there other people? These people are all older than you; were there others?
Others of my generation? There was a man, (Bruck), who became an astrophysicist of some repute; there was an American who didn't know anything, by the name of (Cranford), I think, who finally disappeared. In fact, one of my proud moments was when Bechert told me that I should teach (Cranford) about his subject.
Was the feeling there that the man's difficulties were because he was not very smart or was it expected of Americans that they would not know anything?
No, this was not at all expected of Americans. In fact sometime during my stay there Pauling was there and he certainly was very different. He was generally recognized as really knowledgeable. It may have been quite early. Then at another time Condon and Rabi were there -- I think that was the second year of my presence -- and there was no question about their being smart, so there was no feeling that Americans were stupid. But this particular one was extremely stupid. Pauling may well have been in this first term, I just don't remember. He may well have given one of the seminars.
As you were learning this material in the seminar did you also learn and deal with the matrix mechanics?
No, not at all. Just wave mechanics.
Were there references to it? Again this is a terribly important sort of point for me. At Munich were they just not interested in it until the Schrodinger approach came along?
I don't know what they did the year before. Certainly Sommerfeld found wave mechanics tremendously appealing; this was something he could do. He understood the mathematics, he could deal with the mathematics. I don't think he ever solved any problems by matrix mechanics. We discussed Schrodinger’s paper in which he established the relation with Heisenberg, but that was all in the spirit that this was the way one understands Heisenberg. Nobody ever, to my recollection, said, "There is a calculus of the matrix mechanics." Nobody to my knowledge mentioned how Heisenberg got matrix mechanics, that it had something to do with the spectral resolution of the dipole moment of an oscillator or something like that -- never. At a much later time, I think it must have been in early '28 or so, Sommerfeld said, "Well, of course we really believe that Heisenberg knows better about the physics, but we calculate with Schrodinger." But that was very much later.
What was the attitude in this seminar toward the sorts of things that Schrodinger said about the wave function?
In the first go-around I think they were believed, and then I believe a little later people began to realize that you couldn't use that continuum theory. As far as I remember, the seminar never took up Dirac's radiation theory although I stayed with the seminar for two and a half years and the theory was then out. It never took up Heisenberg's mechanics, even later it didn't. As a matter of fact I don't think I learned matrix mechanics until almost when I took my doctor's degree two years later. I then read Dirac's papers. I read a little bit of Heisenberg's papers -- I never read them all. But to really work with matrices, other than just calculating them from the wave functions, I think I didn't learn until 1930 or so.
What sorts of issues then were live for people in the seminar in the beginning?
In the beginning they were just interested that you could now do all this, and one of the fascinating things was the Stark effect--that one could do the Stark effect and do the intensities. There were big debates whether the intensities could really be confirmed. I think the seminar had very little idea what these intensities really referred to and they were disturbed that some of the experiments didn't give the correct Stark effect intensities. They don't because the P states and the S states and the D states are excited differently. I think this first seminar was simply fascinated by the fact that it now worked.
Did they try it out on other problems?
Yes, there was some attempt to do the heavier atoms. Unsold tried the helium atom, not very successfully; he didn't get the exchange. As time went on I think one of the fascinating things in the seminar was Heisenberg's treatment of the helium atom which was discussed in great detail. Another thing was Davisson and Germer's experiment, and that then was suggested to me by Sommerfeld as something I might work on.
You say that there was great fascination with the Davisson-Germer experiments and yet if you were convinced by the Schrodinger equation, you already knew --
Yes, but I think it is after all very convincing if you actually see it.
But was this needed to convince -- I mean, it would be quite wonderful to see it and yet the question is whether there were people who were now convinced who had not been before in the Sommerfeld group.
Not in the Sommerfeld group; the whole Sommerfeld group was convinced by the Schrodinger equation. But there was Wien and a few other experimentalists who were not very well convinced and they were then convinced by the Davisson-Germer experiment.
Including Wien himself?
Including Wien himself.
There apparently was a meeting before you got there, at which Schrodinger spoke. He said something about his new theory for which Heisenberg criticized him and Wien then was very much upset. Were you in Munich, perhaps even in the spring there?
This may very well have been just before you got there.
Yes, that could well be, yes.
These early computations on the helium atom could have been quite discouraging because clearly one needs the extra idea there and one may think in absence of the extra idea that it isn't going to work any better with the new theory than it did with the old. How did people feel?
I think Unsold felt, and Sommerfeld probably agreed -- but about that I'm not sure -- that he had not done a good job and that he had not really solved the six-dimensional equation. I think what he had done was some cheap 'Hartree' and very cheap 'Hartree' and this wasn't very good. So I don't think he was really discouraged.
What about spin?
What I remember is that this was considered quite a mystery. I think there was a seminar on the Klein-Gordon-Schrodinger relativistic equation' and this was pursued to the bitter end. One of the things in the seminars was that everything was done explicitly including all the algebra, so you could just follow the seminar and then you knew all there was to know. So this was also done for the Klein-Gordon equation and then I think at the end Sommerfeld or Wentzel made the cryptic remark, "Well, so this doesn't agree with experiments, but then we are told there is spin so the spin must make it right." This was before Pauli and I think -- I'm not sure, but I believe that then Pauli's paper about spin was discussed when it came out. But spin was essentially discussed as something too difficult for us to understand.
Did you discuss it just as a spectroscopic tool, the new ways of labeling?
Just as a spectroscopic tool, yes.
Did you still learn to do spectral analyses with half quantum numbers, to do term analyses with spin?
I did because I had read Sommerfeld's Atombau and I was always somewhat interested in it, but I never did any spectral analysis.
But was this still an issue at Munich in the time you were there? Until just before you got there it would have been.
No, no, it was not. Very soon, after Schrodinger and the Davisson-Germer experiment, Sommerfeld got interested in the theory of metals and then I think almost the whole interest of Sommerfeld and the seminar concentrated on the theory of metals. As far as I remember -- I said that once before -- Dirac's paper on radiation theory was not discussed. Then I left and so did Sommerfeld; I took my PhD in July '28, Sommerfeld went on a trip around the world, and I came back a year later.
You went back to Frankfurt for a year.
I first went to Frankfurt for half a year and then to Stuttgart for half a year. As far as I remember, the Dirac equation was never discussed in the seminar as long as I was there.
That really is fascinating.
Yes, quite strange.
I want to be clear because I realize now by the time you left the Dirac electron paper was also out. It came out very early in '28. But it was not that that you meant; it was the earlier radiation theory papers, the derivation of the dispersion formula and so on.
Yes. Well, I read those but they were not discussed in the seminar.
Did others also read them? It's hard to understand those not having been more exciting to the group there. How would you account for that?
I don't really know, but I think Sommerfeld was so fascinated with the theory of metals which went back to his early years, his early attempts. He was just busy; he wasn't interested any longer in the rest of quantum mechanics until much later.
Well, this must mean that if the interest of the seminar was switched almost exclusively to theory of metals, it also means that they nearly stopped reporting on papers, because there weren't that many other people writing papers. It must have been reports on work that the individuals were themselves doing.
Yes. Sommerfeld himself gave a course on his paper on the theory of metals while he was writing it and this was very good. Then afterwards there were such people as Houston who worked on it--who else was there? -- there was another man.
Heitler may well have been, I realize, in that seminar.
No. However, I should have mentioned that the Heitler-London paper was discussed in great detail and again as a great thing; so it was all concentrated on solving the problems of the atom, then the molecule, then the solid state and not finding out more about the foundations.
What, for example, was the reaction to the Heisenberg uncertainty principle paper?
Not very deep.
Was it interesting? Had these problems bothered people?
No, these problems had not bothered people; at least it was not evident that they had bothered people. The paper was discussed, so that was it; this was a 'fine conclusion.'
But not a conclusion to anything that had really upset people previously.
No. It should really have been discussed as the thing which now finally solved the paradox, but it wasn't.
At certain other places, of course, it was.
Entirely. Copenhagen, certainly.
At Copenhagen in a very lively way and at Gottingen also.
No, it was not hailed as the solution to the great puzzle.
Were there great puzzles?
No, there was no great puzzle and I think this is the greatest characteristic of the Sommerfeld group; we were not made aware of great puzzles. We were given the impression that here was a wonderful tool. Now you could do things, now you could solve all these interesting problems like all the complicated atoms and so on and chemistry, but fundamental problems, no. I should, however, mention scattering. Sommerfeld was interested in scattering. He was interested in Born's paper on scattering.
Was it that, do you think, that, also convinced the group that one could not adopt Schrodinger’s interpretation?
Yes, yes; it certainly did.
I want to make certain that we are understanding each other here because in some places people say, "Yes, I suppose that paper must have convinced us but I think we already knew it." Now what I'm really asking is, is it your impression that this paper was important in producing a transition?
I think so. Certainly in Sommerfeld's group, but this may have to do with the unquestioning attitude, as far as I remember. Now I was what one would here call a first year graduate student, so I probably wasn't present at some of the more profound discussions but as far as I remember from the seminar there never was any real worry about the Schrodinger continuum idea, that two states exist simultaneously. I don't remember that this was questioned.
At the more technical level, in the early Schrodinger papers there are about three different ways of getting the wave equation, the first of them still almost incomprehensible. Did this bother people? You know, in the first paper he uses a variational method and I still don't know anybody who feels he's quite made sense out of the variational method.
Which is different from the way the variational method is now --?
Yes, in part because it's pulled very much out of the hat and in part because it depends on some very odd substitutions and variance conditions. No, it is not what one would now call a straightforward variational derivation of it. Then he later gets very deeply involved with the question of the parallel between wave optics and geometries, doing classical versus wave mechanics as the parallel to geometric versus wave optics. Was this again too fundamental to concern people?
I think so. Now the analogy between classical and, wave optics very much appealed to Sommerfeld; he liked that and I think he considered this a sufficient derivation. That was my impression. It didn't impress me terribly much but it seemed to impress him. The variational I don't remember.
But largely then it was a matter of driving forward on the solution of problems. This of course fits very well with the whole tradition of the school, as you say.
But you're the first person I've discussed it with in this period and it's fascinating to see it holding up that well.
I am; I think, one of the very few who was there during that period. You might ask Pauling who I know was there.
I'm hoping also to talk at some length with Wentzel.
Yes, Wentzel of course is an extremely good witness for that period and probably very much better than I because he really was grown up at the time and did it very consciously; he's probably the best.
I find when possible one wants to go over these things with two or three people who were there.
Yes. Now Wentzel left while I was getting my degree, I don't remember exactly which year, but in the crucial period he was there. Let me see -- I think you characterize it extremely well: "driving forward with solutions".
Again at the level of fundamental problems, what about the transformation theory of Dirac and Jordan?
No seminar discussions?
No seminar discussion.
That's really fantastic. This whole set of problems just left people cold.
Yes, yes it's --. I remember I gave the seminar on perturbation theory which seemed quite straightforward and that appealed to Sommerfeld very much.
This was on the Schrodinger paper in which he does the Stark effect?
Now your impression is that very quickly Sommerfeld picked out the theory of metals and that then this was the problem for almost everybody in the group. How did you happen to avoid that yourself?
Well, I think it isn't quite fair that he picked that out exclusively; he did quite a bit about scattering and particularly Bremsstrahlung. Just exactly when he -- I think that came after the theory of metals. I avoided it mainly by getting my thesis assignment before he got really interested in this and before he knew how to do it. He told me, "Now, why don't you look at Davisson and Germer; there are some discrepancies and also it would be nice to understand a little more about it." That's about all he told me. He gave me a hint that I should look at Ewald's papers on X-ray defraction so that I did and found them very useful; my thesis is very much patterned after Ewald's dynamic theory which was his thesis. I found rather quickly the refractive index and then much more slowly developed the dynamic theory which I couldn't solve, which also nobody has solved since then. I felt very stupid that I couldn't solve it but I know now that it isn't all that easy. I should have stopped with the first approximation which was good and had the form factor in it and it would have been a much better paper.
Did you make any attempt also to take this over and do any of the collision problems or the Ramsauer effect which is tied up in its explanation with the Davisson-Germer?
Not at that time. I then went back to collision theory later on in 1929-'30 and wrote about inelastic scattering of electrons using Born's paper and that was my Habilitationsschrift. But at that time I didn't try anything else.
As all of this was going on were you going to some lectures, learning some more physics and mathematics?
Yes. I took all of Sommerfeld's courses. He again goes through the usual cycle. Then I took some mathematics, not terribly much actually -- theory of functions, that is complex variables.
Every student of Sommerfeld's took that didn't he?
Yes, which after all is a very fascinating subject. I took a course in thermodynamics from Carathéodory who was a great mathematician which I found quite unpalatable.
Was it the approach or the subject?
The approach. I just am not a mathematician. I just don't have the patience in that. If it had been in this country, I would have listened to the end; since it was there, I just gave up half way through. Then I heard physical chemistry from Fajans which I found quite interesting although I don't believe that it was all that good. I didn't take terribly many courses any more; I took these and Sommerfeld's courses and then all the theoretical physics that were offered by the younger people. I took an advanced laboratory, Wien's lab.
Were relations between Wien's lab and Sommerfeld's group any better by this time?
Not too bad. Wien came frequently to Sommerfeld's seminars.
Yes, not regularly but I would say two or three times a term at least or maybe a little more. I tried to attend an experimental physics seminar but gave up after two tries because they were both 'Quaker meetings'. Wien wasn't there but the two ausserordentliche Professoren mostly sat there silently and contemplated the puzzle of some strange fact which had to do with some stop-cock grease problem which I found extremely uninteresting. It was definitely uninspiring. I found the advanced laboratory quite interesting and got through two terms of that and then quit. Then I must have read quite a bit because Wien was very satisfied in the exam; I think I was the only theoretical physicist to whom, he gave an A in the exam.
I'm interested in how much experimental work you went on doing.
Not terribly much.
But more, I think a good deal more, than most of the people doing theoretical physics during this period.
Yes, but considering present day training, I did very little; I did a few experiments with high frequency electric currents, a Lecher system if you know what that is -- two parallel wires determining the nodes of the standing waves. And I did the characteristics of electron tubes and one experiment which was a dilatometer using interference fringes to determine changes in dimensions, and the oil drop experiments -- things which nowadays are certainly sophomore lab or something like that.
Were those set up the way they so often are now? I mean, would you go in and find the apparatus all there waiting for you just to turn the switch and to follow the directions?
Not entirely, but pretty much. I don't think I could have done it otherwise. They were pretty much set up but you had to gather a few things together; it was sometimes not just turning the switch but it was quite straightforward.
Has that training, do you think, been of any help to you?
In what ways?
Well, I think I know a little bit how well you can do experiments, what troubles you get into, what accuracy you can expect and so on. I am very fond of designing experiments, interpreting experiments, and I think I know, a little more than most theoretical physicists, what can be done and what cannot be done. I haven't done a single experiment since my third year of studies but at least I know that --.
You spoke of the great interest that the Heitler-London paper had created. What about the introduction of group theory?
I don't remember that there was any seminar about it. However, I have the impression that it created some interest. Now I'm not very positive about this. I read the Wigner-von Neumann papers quite religiously and I think there may have been a seminar or two about it.
But you acquired this technique right away, did you?
I didn't acquire it well enough so that I could use it on spectroscopic problems, but well enough to understand the papers; and I found it very --.
When did you learn it?
You mean to use it? The next year when I was in Frankfurt I studied a group theory book by Speiser which is quite a good book, and then I found that the best way to go on was to solve one problem by group theory, so then I wrote the paper on the splitting of levels in a crystalline field. I don't know much group theory to the present day and. I'm afraid of it except for very finite groups; finite symmetry groups I more or less know how to handle but I'm afraid of the rotation
(cont.) group even to the present day. At one time I understood what they were talking about, but that's about all.
There was, as you know, a good deal of resistance to this elaborate mathematical technique in certain places. A lot of people have told me, "Well, we figured out that there was another way to do it and it wasn't until '32 or '33 that I learned group theory." Would that have been true at Munich?
I don't know. I just don't remember. I don't think anybody at Munich ever did anything about group theory; I'm sure that Sommerfeld was aware of these papers and I think he approved of them as something that he didn't need to do.
How about the von Neumann statistical --.
This was again too fundamental. When did the field theory problems begin to become interesting at Munich, or was this already after you left? I mean, nothing had been done with Dirac at all, you think, in the time you were there?
Well, when I returned to Munich in the fall of '29 I found no great interest in these problems.
You had still not gotten very deeply involved with them yourself, had you?
Well, I had read Dirac's paper on radiation theory. I had read the paper on the electron which I found hard to understand, and I read Darwin's paper which I found easy to understand.
Yes, that's right; Darwin's paper is the one that does the exact solution for the hydrogen atom.
So, all right, this was certainly quite understandable. I don't believe there was very much interest in Sommerfeld's group except that now the correct formula had been obtained, so that was recognized. I think there may have been a seminar on that solution but I don't, remember it.
What about the whole technique of space quantization -- the Jordan paper and then the Jordan-Wigner paper.
No, nothing, Second quantization --. Nothing at all.
But there was that whole series of papers: Jordan-Klein, Jordan-Wigner. And then what about the field, theory papers which then -- Heisenberg and Pauli?
Nothing. That was all too difficult.
Too difficult or not worth the time?
Well, it would take a very great amount of time and perhaps somebody would find an easier way. Now Heisenberg-Pauli certainly has been simplified slightly.
I don't mean that it isn't a hard paper; it's a terribly hard paper. I don't begin to understand it.
Yes, and Fermi's version later on was very much simpler.
It was really that that brought you into this part of the field.
Had you tried particularly before?
No, I had not. I was pretty much interested in the things you could do directly with the Schrodinger equation. Now in this I think I went farther afield than Sommerfeld's people generally went, especially to the collision theory. One thing that fascinated Sommerfeld was the use of contour integration to show that you've got outgoing waves. When you did a straightforward perturbation theory for, let's say, the photoelectric effect and then summed it all up with contour integration you got outgoing waves. That he liked.
Was there still any sign in this period in working with Sommerfeld of the thing that so many of the people who had worked with him in the five years before you got there described as number mysticism, number magic? It had of course done magnificent things for him in the period up until about '23-'24.
No, there was no sign. I think he really was convinced that the Schrodinger equation was right so now one didn't need number magic any more, now one could just exploit it.
For him it is right back to the beginning of his, career again with the Maxwell equation.
Because the contradiction -- or to me the sense of contradiction -- between that early work and the things he does so magnificently in the late 'teens and early twenties and then his going back again.
And he felt very happy about coming back.
Did he talk about that sense of happiness?
No, but it was evident; it was evident that he was able now to use the techniques he liked and could do well to do things which he knew were important and where he wanted to know the answer.
As we have talked, the things you've told me about Munich fit very well with things I have heard before for the older period. But it is clear that from the point of view of somebody at Gottingen or at Copenhagen, there are all sorts of exciting things going on, big issues, that simply do not exist really, or scarcely exist, for people in Munich.
They did not exist and looking at this period from five years later I had the impression that I had really missed the development.
Where did you pick up these other problems?
I think really at Fermi's place -- yes, mostly at place. In early '31 and '32 he was in the midst of the problems that were really interesting and also he had the completely different view of physics, the qualitative approach. Sommerfeld had very much the quantitative approach. Nobody in Sommerfeld's place would write down orders of magnitude; you had a problem, you did the problem, and then there was the answer.
This is clearly another way of doing physics. Was Fermi, himself ever at all concerned with the sorts of problems that so worried Bohr still in this period?
No, he was not and I never really got exposed to these problems. Much later, in '33, I finally knew that people were worried about these.
How may people besides Bohr himself were still worried. Einstein, of course, and Schrodinger.
Very few people were I think -- Rosenfeld was; I don't think Heisenberg was worried -- I don't think Pauli was. No, it was mainly just a very small group of people directly working with Bohr, and then the antagonists -- Schrodinger and one other reputable person who joined that.
In the early '30's. I'm not sure who that would be -- de Broglie himself comes back to it through Schrodinger; of course Einstein -- I'm not sure.
Probably I meant de Broglie. It never worried me; in my early education I never heard of these problems and later on they had been solved.
When you did get involved through Fermi particularly and the Fermi paper with problems of the field and of the interaction of radiation and matter in more detail, is it by then clear that this is not going to work out well? Or was there still a good deal of optimism?
No, we had a good deal of optimism when we wrote that paper. There were the divergences, quite obviously. Fermi wrote his Physical Review article just about the same time and that made it perfectly clear, but there was a lot of optimism. It was nice that you could do at least the two electron interaction in this first approximation many different ways and get the same answer. I don't believe the optimism quite disappeared. I remember in '37, it must have been, when Weisskopf came to Rochester, he got the divergence down from linear to logarithmic, which was very interesting and so, 'Maybe if you try a little harder you will get it down to nothing, to convergence.' I don't believe that it was quite settled until the war. I think everybody would have agreed that the chances were small that you would succeed.
I'm curious about one other thing which really takes us back. You start on advanced physics just in the year one finally cuts away. Now, to what extent then did one go back?
I didn't go back at all. I heard that people had been terribly confused and Sommerfeld mentioned it from time to time, so did Wentzel, but these things are better forgotten. I don't think, that I ever looked at one of the old papers until 10 years later.
What about certain of the advanced subjects that would have been standard just a little bit before, like Hamilton-Jacobi theory for example? Did you ever do the sort of thing that one 'had to do'?
At one point and I think quite late I learned Hamilton-Jacobi theory in order to present it to my class in Cornell but I never did anything with it. I never used it for old quantum theory calculations; it never fascinated me.
It wasn't something you still had to know in order to be a 'licensed theoretical physicist' in '28 already.
Why did you present it to your class at Cornell?
It is in mechanics that I present it. It's a sort of crowning glory of classical mechanics. I don't always present it in my mechanics course and certainly not as the foundation of quantum mechanics. The thing I hoped to learn about Munich--and this is concerned with problems at the level of applications of the Schrodinger equation rather than with fundamentals--would be some points of dispute, of argument, of particular excitement because lord knows those first years you were there were full of them elsewhere. Now it may well be that this was being hidden really by the fact that what one was after all trying to do was to apply the Schrodinger equation.
Your impression is that there were not points at which people were really at cross purposes over the interpretation of problems or this sort of thing, but that the excitement was always, "Here is a way to handle --”
"-- the problems that we have tried to handle for so many years," yes.
There was one dispute, that I still know very little about, which carries on in the literature and between people for some time in the new period. It comes out particularly in the approach to molecular problems and is, namely, approach through molecular orbitals versus the approach through exchange integrals. Did you run into this one?
Yes. I ran into this one to some extent and it was discussed to some extent. It interested me personally and was closely related also to the Sommerfeld metal theory because there you take completely the approach of orbitals. I was worried about it personally. I wanted to find out but I didn't ever find out anything very interesting; but yes, this was an interesting problem.
In retrospect many people would say that after all these were just two different approaches to the same problem. At the time it appears that there were plenty of people who did not recognize it as this and who really were upset because the other person was doing it wrong.
No, I think I would partly disagree with the statement that they are two different approaches because take the hydrogen molecule. If you take the orbital approach then you have from time to time an H- and an H. If you take the Heitler-London approach you always have H and H, and this is not the same thing and it isn't the same thing today. Mott has said this is really the fundamental problem of solid state physics because when you have separated atoms you clearly have atoms and not ions and when you have a good conductor assembled you clearly have orbitals, so where is the transition and how is the transition? The problem has not been solved even today.
I wouldn't have thought of it that way. That's not so true of the molecular problem; I mean, one would hate to have to say that for this molecule it occurs exactly here. There are enough areas, as I understand it, in which one can get the same result by either way if one will hold enough terms.
Yes. Take sodium chloride: when they are together you certainly have something very close to Na+ and Cl-. So when you put it in terms of potential curves, you may talk about potential curves crossing at some point, but you have to use both potential curves and it's not just the one curve. It was not clear to us in fact at Munich and one of my theses in becoming Privatdozent--you know you have to write down a number of theses and defend them -- was concerned with this. I don't know what I said; it probably was wrong, but it was concerned with the problem of polar-nonpolar, Heitler-London, versus (???).
Who for you would have been the main source of the orbital approach at this point? Would it be the metal theory?
Yes, metal theory, the Bloch theory.
Who else was deeply bothered about this? Do you remember?
Who at Munich? No, I don't think I do.
I gather on occasions there were some quite hot and difficult exchanges over this issue. Apparently there was a meeting at which both Hund and London spoke and at which there was a good deal of disagreement and a failure to come to terms.
No, I don't remember anybody who was very excited about it. I think Sommerfeld was quite satisfied in accepting the orbital approach for the metals. In fact he didn't even care terribly much why the electrons were free, which I thought was a very important thing to know, and I believed the whole theory only when Bloch's paper appeared but he believed it just because it agreed with experiment.
Did you see a great deal of him?
Quite a lot. First there were the seminars, and then in my later years, just before I took the degree and especially after I returned, I was some kind, of assistant to him. I think I would have a discussion with him maybe once in two weeks or so. In the early years I didn't see much of him aside from the seminar. I saw him once when he assigned the thesis and twice while I was doing the thesis and not much outside of that. Well, there were occasional outings when we went to the café in the Hofgarten but I don't think I was involved in that until I came back, and that happened maybe two or three times a semester.
I had. the impression that perhaps in the period before you got there students often saw rather more of him.
Yes, I think that's probably true.
I know Heisenberg saw much more of him than this from the very beginning and I had the impression that he may at that time have been simply around the group more often than when you were there.