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Oral History Transcript — Dr. Alfred Lande

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Interview with Dr. Alfred Lande
By Thomas S. Kuhn and John Heilbron
In Berkeley, California
March 7, 1962

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Alfred Lande; March 7, 1962

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 ca. 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: Ernst Back, Niels Henrik David Bohr, Max Born, Constantin Caratheodory, Peter Josef William Debye, Paul Ehrenfest, Albert Einstein, Walther Gerlach, Samuel Abraham Goudsmit, Werner Heisenberg, Heinrich Mathias Konen, Peter Lertes, Fritz London, Erwin Madelung, Wolfgang Pauli, Max Planck, Erwin Schrodinger, Arnold Sommerfeld, Otto Stern, George Eugene Uhlenbeck; Artillerie Prufungs-Kommission, Universitat Gottingen, Universitat Marburg, Universitat Munchen, Universitat Tubingen.

Transcript

Session I | Session II | Session III | Session IV | Session V

Kuhn:

[A discussion of the contemporary awareness of the tentative character of the old quantum theory and of the possible routes for ‘going deeper’ is here omitted.] [Returning again to the note in Naturwissenschaften] Do you remember conversations from those days or seminars that attempted to look at the state of the field, that expressed this discouragement more concretely?

Lande:

I don’t remember seminars, but I remember that in lectures and presidential addresses and so on, this point of view was always emphasized by great physicists. I think you can gather dozens of examples of this point of view.

Kuhn:

In the printed literature we already know of a number. To what extent can one find more this way -- things that have not gotten into print?

Lande:

No, when Einstein or Bohr or Planck said something in an academy address the same thing was read by everybody and repeated.

Kuhn:

Did the Compton effect generally, in your own recollection, make a considerable stir when it was known?

Lande:

Oh yes, of course.

Kuhn:

Then there was much immediate discussion of it.

Lande:

Yes, it was one of the principal experiments, the crucial experiments in quantum mechanics.

Kuhn:

Was there in Europe anything that resembled the debate that went on here between Duane and Compton?

Lande:

I don’t remember that.

Kuhn:

How about de Broglie’s work, was that much known in Europe?

Lande:

It all came to be known rather immediately after it was published. But there I also have a certain item. De Broglie and Schrodinger were not the only ones with such ideas. I told you this anecdote about Debye being so very skeptical about it, and rejecting this as almost nonsense. I was in Frankfurt at that time, and I was assistant of Professor Madelung. He was a very deep thinker, who was always full of ideas, but because he was a little bit too expansive, did not work them out. He had one idea worked a little bit, and suddenly he had a flash of something else. So he had the brains to be one of the very great physicists, but in some way he didn’t have the energy to follow up. Madelung worked very seriously on a kind of wave theory of the atomic levels. I do not know much about details -- what he did -- but he certainly was on exactly the same track as Schrodinger. In 1923 already, at the same time as do Broglie’s work came out. This was just the time when I went from Frankfurt to Tubingen. No, to correct the dates, this must have been even earlier.

Kuhn:

Was any of that work published?

Lande:

No, no… He didn’t explain. He only told me he doesn’t believe in these orbits being real -- it must be something wave-like. Then de Broglie’s paper came out. Then he gave up -- he had another idea. Schrodinger just began there, and achieved a very great deal. It is very interesting to see the personal character having such an important role in making discoveries.

Kuhn:

When you say that the de Broglie paper was immediately known throughout Europe, this is a very puzzling point for us.

Lande:

My personal recollections are only that this paper of de Broglie was such a striking innovation and something so obvious and so simple to demonstrate, to everybody, even if he didn’t know much about quantum theory, that it made an enormous impression on everybody immediately.

Kuhn:

Do you remember any discussions of that paper?

Lande:

No.

Kuhn:

It wasn’t terribly widely circulated.

Lande:

You see of course the Germans at that time did not widely read the French literature. This paper of de Broglie appeared in a thesis -- that means almost as a private print for the Sorbonne. It was then published in Annales de Physique. The moment it was published in Annales de Physique someone in every country discovered it. There was always someone who reads outlandish journals. Such a striking thing doesn’t remain secret for a long time.

Kuhn:

What about matrix mechanics? Do you remember how you first heard of this, or any of your reactions or those of the people around you?

Lande:

I first heard of matrix mechanics when Max Born was in Tubingen either at the time when he had sent off his paper already or maybe even before. And he told me something about it; that they had a completely new approach to quantum mechanics and everything is dominated by matrix multiplication and A times B differs from B times A. I didn’t understand a single word about it. And I don’t think that Born and the whole group in Gottingen “understood” much more than the mere formulas.

Heilbron:

Had you run into matrices during your time with Hilbert, or earlier?

Lande:

In my early classes in mathematics of course there were determinants and other matrixes, but this was all. Nobody understood what this means as a magic way. I remember also that t this time I had just finished the 2nd edition of a little book in German on present-day quantum mechanics, which appeared at Steinkopf. Before it went to print there had already appeared this paper of Born, Jordan, and Heisenberg, and I made a small Nachtrag -- simply also the formulas, without any comment. I remember that Planck, who knew of this new edition coming out, wrote me a letter or postcard in which the passage appeared, “I wonder what you can make of these matrix formulas.” He couldn’t make out any more than anybody else… It took years before we could understand more what this means. To add my purely private opinion, what it really means and why there is this matrix calculation and all has interested me for 35 years, whereas most people have simply acquiesced with it. In my latest work, I think I can explain why all this is, why there is a wave equation, why there is a periodic relation between p and q, and in short, I think I can explain from simple postulates of invariance and symmetry why, if there is a probability scheme at all, this probability scheme must be just this one which we have. But this of course belongs not in the 1920’s but in the last few years.

Kuhn:

If people generally felt that all they could see was the formalism, did they nevertheless feel that there must be something quite fundamental in it, or were they very skeptical about the whole thing?

Lande:

It came out, and came and saw and won right away, because it was successful. Furthermore it came from Born, who had a very good reputation it came from Heisenberg, who had a reputation of being a genius, so how can it be wrong? But everybody said, “I don’t understand a work, but I apply it.” And this attitude is still very much prevailing. I can quote you a passage which Professor Dyson of Princeton printed about two or three years ago in an article in Scientific American about the foundations of quantum mechanics, in which he said about the following, “The student who is introduced into quantum mechanics first worries very much because he does not understand what he is doing. He is simply told that there are these and. these rules, apply them, and they are successful. This stage of worry lasts usually from 3 to 6 months, or longer, until the student suddenly says to himself, ‘now I understand quantum mechanics,’ or ‘rather I understand that there is nothing to be understood.’ And from there on he is happy again.” Now Dyson writes this not only about the students, but it is his attitude. There is nothing to be understood. Apply rules, obey, and in this way make your career. I don’t see any difference between this present attitude of most physicists from that in the first month after the matrix mechanics in Schrodinger’s equation came out.

Heilbron:

Of course there is a lapse of time between --

Lande:

There is a great lapse of time, and nobody took the trouble to ask why are these very strange quantum rules. And the reason is that nobody took the trouble because the Pope in Copenhagen said, “Don’t worry. Be satisfied with the tautological word ‘duality’. Why are people poor? It comes from the poverty. Is there a contrast between wave and particle phenomena? It comes from duality.” And this verbal solution of the problem has prevented and hampered the progress of real understanding for 3 years. But this is my purely personal position because I have worried, not between 3 and 6 months, but between 30 and 35 years about the quantum problem.

Heilbron:

I was thinking of the shorter lapse of time between the publication of the Born, Heisenberg and Jordan papers and the appearance of Schrodinger’s work. And it’s easier to take the matrix mechanics when one has the wave mechanics and someone points out the connection, but I was wondering about the degree to which people accepted and applied the matrix methods before the Schrodinger equation.

Lande:

Well, all this happened so very fast -- there was matrix mechanics, there was Schrodinger’s equation, and a very short time after it was shown that both are essentially the same. The Schrodinger equation is a little bit less general than the matrix formulas, but it is the sane. This was shown first by Schrodinger himself, and then by Eckart, and I don’t know who else… Let me say this, there are those problems in which there appears a continuous variable like x from minus infinity to plus infinity, and momentum, and energy can have any value -- in all those cases the treatment by a continuous wave equation is so much more practical. Whereas there are some few problems -- problems of space quantization -- where the matrix method is more to the point… They came almost at the same time, and people simply said, “Now finally we see the light although we don’t understand at all.”… People of course liked the wave equation much better immediately because the technique of the differential equation is known to everybody, and one could see how, the whole thing worked.

Kuhn:

Did that continue to be the case when the Dirac formulation of the wave equation arrived in ‘28?

Lande:

Dirac again came out with such a great success that one simply accepted his formal approach, and there was not much discussion. It came out perfectly. Of course there were intermediate steps -- Pauli’s approach with 2 times 2 matrices. Then Dirac with four times four came, which was relativistic, because everything should have four legs in relativity theory instead of three.

Kuhn:

Yet there were all the problems about negative energy states.

Lande:

Yes, this came later, this was worked out. Then paradoxes appeared one after the other, but it didn’t touch the fundamental equation. So we still struggled with these paradoxes of the Dirac equation, and its solution -- there is an underground of already filled states. Everybody’s so used to it that there’s no use of arguing about it. To me it seems a very easy excuse; something we didn’t know.

Kuhn:

How did people, and you particularly, feel about the spin when you first saw or knew of the proposal? Well, this idea is one you must have heard of before the Goudsmit-Uhlenbeck paper actually appeared.

Lande:

Yes.

Kuhn:

And had you heard of Kronig’s --?

Lande:

Yes. Kronig was in Tubingen when I was there, and he studied films of Back -- the Back-Zeeman effect -- and studied multiplets. I didn’t hear anything from him about spin, but he probably was on the track of it. But you find all this in great detail and. much more authentic than I can tell you in this article by van der Waerden… And then also in this article by Hund in the Heisenberg Festschrift. Only one item again. The doublets are due to this and that position of the spin axis, as it turned out later. I was invited by Ehrenfest about this time to Leiden. It must have been after the g formula already, because it was on St. Nicholas Day, when I came into the hail they had on the blackboard the g formula out of chocolate letters so this fixes the date. But it was before the spin, and I remember that Ehrenfest and someone else, who probably was Goudsmit or Uhlenbeck, I don’t remember, questioned me, what do I think about the doublets being inverted, the doublet energy levels being inverted. The upper one here -- it should be the other way around according to the theory that the Rumpf has magnetic moment, and there is orientation of the large electron in the Rumpf. And the fact of course is that this inversion of the doublet is against the expectation of the large electron in the magnetic field of the Rumpf. It is explained that it is not the Rumpf but the lodged electron itself. But they asked me, “What do you think about this being in?” And I said, “Oh, I don’t know, some reason will be found.” This is the attitude -- you make a certain step, then you rest. The next one? Weil, it will be found out in due time. And apparently the people in Leiden had the idea of the spin already, including this detail. A magnet running around a circle would give in its own field an inverted doublet. From which follows that the spin idea was not simply an explanation of the doublicity and multiplicity as such, but went deeper into such details as the arrangements of the multiplet lines…

Kuhn:

Kronig speaks of a visit of both himself and Pauli to Tubingen in 1925, I think January ‘25 or the end of ‘24, at which there was apparently a good deal of talk.

Lande:

There wasn’t much talk because Tubingen at that time was a small university. There was one experimental physicist in charge of the whole laboratory -- Paschen. There was Back, his assistant. Back at that time wasn’t even a Professor, only an assistant professor. And one theoretical physicist -- this was myself -- and this was all. I didn’t have anyone to discuss things with.

Kuhn:

Sam Goudsmit has very little of his own correspondence left, but he has been looking through it; and he has a card from you, dated January 1925, which says that Kronig and Pauli had just been to Tubingen and that there was much interesting talk. I just wonder whether there’s anything left to be discovered about what may have gone on at Tubingen on that trip.

Lande:

I remember a visit of Pauli to Tubingen which however came immediately at the time of the exclusion principle. Could this have been the same visit? Probably not… I remember Pauli being in Tubingen. Apparently at that time he was already looking for confirmation of the exclusion principle. He found some spectrum of Back’s in which there was a line missing which should have been there, and the reason that it was missing was of course the exclusion principle. And he stayed in my home. We had a party at night, and after the party Pauli worked on in the kitchen, and the next morning be told me about the exclusion principle. So I claimed that he discovered the exclusion principle in my kitchen’. But there are seven other cities with seven other physicists who also make similar claims.

Kuhn:

You didn’t know when he started out on the films what he was looking for?

Lande:

Well I did in the same day, in the morning.

Kuhn:

You don’t remember Kronig’s being there with Pauli?

Lande:

I remember Kronig’s being there, but I don’t associate the two. But if there’s a postal card, it must be… So Pauli must have been at least two times in Tubingen apparently.

Kuhn:

Could we talk a bit more about the years at Frankfurt and about the transition to Tubingen. You, I take it, went to Frankfurt with Born? And worked together.

Lande:

Yes. Born was there already and then I came to Frankfurt… Here is Frankfurt, and I stayed in a coeducational country school where I taught mathematics to girls and boys, and also gave music lessons. But at the same time I habilitated myself -- this s a technical expression -- in Frankfurt. Once a week I came over and gave my lectures, until I finally settled in Frankfurt. Did you ever hear of the Odenwald Schule? This is one of the famous progressive educational schools where I went immediately after the war; I threw away my uniform and I went there… The war ended November 1918, and in January 1919 I began my first position after the war.

Kuhn:

And then by the following fall you were in Frankfurt, the fall of 1919, you were already at Frankfurt?

Lande:

I was always in contact with Frankfurt.

Kuhn:

Was positivism in the sort of philosophical education or scientific education that people like yourself got?

Lande:

I had observed very often since Einstein’s discovery -- I had heard it from Born and many other people -- that the main object of physics is not to think about models like the ether, which apparently failed, but to describe correctly. The same attitude was of course violated by Bohr’s orbits, but Max Born for instance was one of those who always were of the opinion, “We must get rid of superfluous elements in our pictures and try to describe as simply as possible.” Already during his days in Frankfurt, I remember this positively. Then from Frankfurt he went to Berlin, from Berlin finally to Gottingen. Is that right? No.

Kuhn:

Do you remember this same sort of attitude toward the goals and tasks of science in people other than Born? Did your teachers in school say that sort of thing about science?

Lande:

No, philosophy was taboo, absolutely taboo. The general attitude among physicists was “Philosophy is bunk.”

Kuhn:

Did this make any problems about their being in the philosophy faculties at the university?

Lande:

No, this was just name, another room, another section. Philosophy is bunk… Much was of course appreciated very much, but nobody paid much attention to him -- at least not the younger people. Some of the older people who had lots of time once in a while took another book and read in it. I was a kind of exception. I not only studied physics for a scientific career, but also made an exam for teaching physics in high school education. And for this difficult exam, I had to listen to a lecture -- history of philosophy -- and also write a small treatise on some philosopher of my choice. I chose Schopenhauer on the advice of my father, who was a very great Schopenhauer fan. He was a lawyer, but he admired Schopenhauer. This was very much against my will. I didn’t want it at all. But I had to read the works of Schopenhauer, and make a kind of thesis on it. But this thesis is gone; I don’t have it any more. So this was my contact with philosophy, and I found out that it isn’t all bunk, but very interesting. I think this was a very fortunate incident, because it gave me a little bit of knowledge of the philosophical questions about reality. All these questions were never even touched by -- let’s see -- 99 per cent of my colleagues.

Kuhn:

At Frankfurt there was really a larger group then, wasn’t it, than the group you were going to go to in ‘22 in Tubingen?

Lande:

In Frankfurt were Born, and Stern, and Gerlach, myself, and a few other experimentalists. But there was constant contact, in particular between us three theorists, Born, Stern and myself, and the mathematicians, too.

Kuhn:

Did many students come?

Lande:

There was quite a big audience, of course, in the general courses on mechanics and optics and electrodynamics and so on. I had as a Privatdozent one of the more advanced chapters with only a small audience, of course. It was the opposite as in this country. The old professors gave the elementary courses because there were many people coming, and the beginners gave the advanced courses. Not very sound I think. Of course the students always had an impression of a great man -- like Roentgen or von Baeyer in chemistry -- same in anatomy. The famous men sat there and they sat at his feet.

Kuhn:

We’ve been looking back, since our first talk with you, at the question of the Stern-Gerlach experiment. We may very well have misunderstood you, but I’ve gotten the idea in our first conversation that this experiment had really begun before you got to Frankfurt.

Lande:

First I was not there. Then I was there once a week. Finally I was there to live.

Kuhn:

Do you remember how Gerlach felt about it? Because it was Stern’s idea, I take it, rather than Gerlach’s?

Lande:

Gerlach came into these experiments at the last moment. Stern had for his help a young assistant, Peter Lertes. He was very energetic and a fine young fellow, who worked with Stern and did the adjustment -- all of it. It was very difficult to have the homogeneous ray and absolutely straight and so on. He worked and worked and didn’t succeed; it always was blurred. At last Stern was really a hit dissatisfied and asked Gerlach also to help, in adjusting the apparatus -- not in anything else. And Gerlach succeeded; really the first pictures came out. When the pictures were out, Gerlach asked me, “What does this all mean?” And I explained to him that this is space quantization of silver atoms. He worked the whole thing out experimentally without understanding what it all meant. Probably Stern had once explained it to him and he hadn’t understood. So 90 per cent of the work was Stern and not more than 10 per cent was Gerlach. And so Stern got the Nobel Prize and Gerlach did not. This other young man -- I still remember him -- Lertes was very upset about the whole thing. He was so to speak “kicked out’ by it. This was one of those intrigue things, you know. He is now chief director of an enormous industrial concern -- the Askania works -- in East Berlin. And is probably a kind of millionaire, or something. An energetic young fellow. But he was “kicked out” -- was what he always said -- in the last moment.

Kuhn:

Was there much discussion between you and Stern and Born in the early days about the experiment?

Lande:

Not much discussion. With myself it came mainly after the thing was done. We talked, “How is it possible that only this and that position is stable and other intermediate positions which should just as well be present,” and so on. This is of course one of the quantum riddles again… We discussed very much, but nobody had any answers, but simply to say, “Well, it’s a quantum rule,” and that’s all…

Kuhn:

Well now Born says in one of his memoirs that he told Stern that he would not get the effect. Nevertheless Born apparently went out and raised the money for the apparatus. It seems so odd -- nobody thought they would get t he effect, but great pains and efforts were gone through.

Lande:

Well you see the same thing happened with Max von Laue. He wanted to set up these experiments together with Friedrich and Knipping in Roentgen’s big institute. Roentgen simply said, “That’s nonsense, for such stuff I don’t give a thing.” And then he went into the very small, limited experimental laboratory attached to the theorist Sommerfeld, who made it possible for Friedrich and Knipping to set up the apparatus. So this seems to be the usual thing.

Heilbron:

If I may ask an ignorant question, what were the theoretical grounds for ruling out an undeviated line? Because if the Rumpf is 1 and the valence electron has also a value of 1, why can’t there be a projection perpendicular to the field direction, and hence an undeviated trace?

Lande:

Well, they -- nobody ruled out anything… Oh yes, I see your question. You mean at that time 1/2 quantum numbers were not yet known. Now we should find out, were they known or were they not? Well, nobody expected anything, but everybody waited. It came out that there were two positions, which could have been taken, or were taken -- I suppose -- to mean that the quantum was 1/2 and minus 1/2.

Heilbron:

You see, it is very curious, because in his paper in 1921, Stern says that if the outer electron was an n orbit, then he would expect 2 n traces, but never anything in the middle. Not 2n plus 1, but always 2n.

Lande:

The application of quantum theory was not quite so known to everybody at that time probably.

Heilbron:

But once only two traces were obtained, do you recall any explanations which might have been advanced to exclude an excluded middle?

Lande:

No. I worked myself, at the same time as all this happened, on the Zeeman effect. Here the term analysis showed that there are 1/2 quantum numbers -- resulting quantum numbers for the whole. But which came first -- this experiment succeeding or my theory in which the 1/2 quantum numbers obviously appeared -- I cannot tell. It was all at the same time. Well there were only a very few people interested in this, a few spectroscopists. The only place where the Zeeman effect was done experimentally was Amsterdam, Zeeman’s own laboratory probably, and in Tubingen. And a little in Gottingen by Runge… Runge himself was trained as a mathematician, was very much interested in number magic, and he certainly tried to solve this riddle. But he also never thought of term analysis. He found at least the Runge rule, which gave us some clue that there is something quantized involved. But in general there was not much interest.

Kuhn:

Do you remember what attracted you to the problem of the Zeeman effect?

Lande:

Why, simply a numerical puzzle.

Kuhn:

Was it the Sommerfeld paper, do you suppose?

Lande:

No, no, before that already. I had studied this book by Konen from the first to last page. There were chapters about Preston’s rule and Runge’s rule and this immediately fascinated me very much, because when you see such simple empirical rules there must be something very simple behind it. But the general interest was very little in this. For instance, Max Born himself had no interest at all. He worked on the physics of crystals the whole time. Everybody at that time -- practically every theoretical physicist -- had studied Sommerfeld’s book, which was a magnificent contribution. Everything explained in a comparatively simple fashion, a great deal of mathematical methods and theoretical physics -- it was one of the great standard works. And so he, and some of his pupils, even if they were not in Munich anymore, were very much interested in working on one problem after the other. That’s the way I came to it. [A discussion of the general conviction in the period that all atoms, as arranged in the columns of the periodic table, were alternately of the doublet and singlet-triplet type is here omitted.]

Kuhn:

On existing experimental data helium might well have looked like an anomaly. It ought to have triplets since it has singlets, it seems to have doublets. Did that bother people, do you know?

Lande:

As far as I remember it didn’t bother them, but suddenly it became clear there must be triplets, and then they also were found by resolution. You see, this would have been such a very special thing, where everybody thought, “Well, it will come out in due time.” And everybody said, “Let’s go on to more important and more general problems rather than worrying about a few spectral lines.” But this whole development all rested on the enormously exact measurements of Paschen and Back.

Kuhn:

What was the relation of those two? Had Back been a student of Paschen’s originally? …

Lande:

Yes. Back originally was not a physicist at all, but a jurist. He studied law, and when he became a physicist before the war? Or only after the war? I really cannot remember.

Heilbron:

The Paschen - Back effect was 1912 or ‘13.

Lande:

But already he was a law student. And the Paschen - Back effect was before the war? During the war he was absent of course. Then he came back and had his grating downstairs in the basement and worked there.

Kuhn:

And the two continued to work very closely together at Tubingen when you were there?

Lande:

Yes.

Kuhn:

What were your own feelings about the move to Tubingen? from Frankfurt?

Lande:

Well, for me it was the beginning; the condition of continuing my career. In Frankfurt I lived only on borrowed time. My small salary as an assistant had to be granted from year to year, and anytime, if I didn’t produce enough I could have been dropped. And I would have been on the labor market.

Kuhn:

Did the money come from the university?

Lande:

It in part came from the university and part from a grant… A private grant. Then after having done this term analysis and corresponding with Paschen and Back in Tubingen, they were very enthusiastic about it. Paschen succeeded against very great resistance to have me called to Tubingen as Extra-Ordinarius -- that means Associate Professor -- which is a life position.

Kuhn:

What sort of opposition?

Lande:

Political. It was the time of ultra-nationalism and Deutsch, Deutsch, Deutsch. It is the forerunner of the Nazi time already there. It was there in the nucleus. Tubingen was the established center of spectroscopy, besides Bonn, where Kayser was the leading spectroscopist. Of course, he was at that time already very old. I met him and he knew about my work. We had a very pleasant talk together once. I don’t remember what year -- 1922 or ‘23 or so. But he was for years out of office, and Tubingen was the center of spectroscopy at that time.

Kuhn:

Did you have a fairly steady stream of people coming there?

Lande:

Well, I remember Heisenberg also was there, as a very young man. I remember him. He came in a kind of Boy Scout uniform to us. And we talked over things.

Kuhn:

Well, you were there when you did that joint paper on multiplets?

Lande:

Yes, this must have been the time. Sommerfeld was once there, and later Born was there. All of them on short visits.

Kuhn:

You spoke before of Born’s great interest in crystallography. Was he generally not interested in atomic spectral problems in these years?

Lande:

No, he was not so much interested. He had his specialty -- what he always called his “old love” -- crystals, and he worked on that. But he always had a corner in his room reserved for general questions of quantum theory, of course.

Kuhn:

Was Hamilton-Jacobi theory part of a mechanics course before the Bohr atom? Did physicists learn Hamilton-Jacobi theory?

Lande:

Physicists didn’t know very much about them. There were universities like Gottingen, in which a number of prominent mathematicians, established mathematicians, and an even greater number of future mathematicians were there as young men and gave courses. And since the older men gave courses on elementary subjects, the more younger men there were, the more special subjects were also treated. So this Hamilton-Jacobi theory certainly was one of those topics. But only in greater universities. In other universities again there was one leading mathematician. Take Marburg -- small university, very pleasant, old university town. There was one full professor, or at most two full professors, and one or two Privatdozents, and that was all. And there was no demand for such subjects as Hamilton-Jacobi theory, in particular, since this was a closed subject. There were courses in higher mathematics, there was perhaps group theory, perhaps number theory, and Mengenlehre or something like that.

Kuhn:

How are physicists really introduced to these techniques? Charlier’s book apparently recurs -- you are only one of several people who speak of it. Was Schwarzschild’s role here important?

Lande:

Not generally. A few people were interested in his work. In general, either you were a physicist and then you went through all of the necessary mathematics as fast as possible and then settled on problems in physics; or you were a mathematician. But courses in mechanics -- I learned my mechanics not so much as a student in Gottingen and Munchen as I ought to hare, but 30 years later when I gave a course in engineering mechanics at Ohio State University. If you teach something then you really have to understand it.

Kuhn:

Good, well unless this suggests something to either you or Mr. Heilbron, I think this might be a good place to call a halt for today.

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