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In footnotes or endnotes please cite AIP interviews like this:
Interview of Paul Epstein by John L. Heilbron on 1962 May 26,
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 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: Niels Henrik David Bohr, Arthur Compton, Peter Josef William Debye, Carl Henry Eckart, Paul Ehrenfest, Albert Einstein, Peter Paul Ewald, Folsom, Kasterin, Felix Klein, Hendrik Anthony Kramers, Max Theodor Felix von Laue, Petr Nikolayevich Lebedev, Hendrik Antoon Lorentz, Robert Andrews Millikan, Walther Nernst, John William Nicholson, Max Planck, Adalbert Wojciech Rubinowicz, Erwin Schrödinger, Karl Schwarzschild, Arnold Sommerfeld, Johannes Stark, Timiriazev, Umov, Theodore von Kármán, Wagner, Hermann Weyl; California Institute of Technology, Rijksuniversiteit te Leiden, Universität Leipzig, University of Moscow, and Universität Munich.
In Munich I did not attend any of the “undergraduate” lectures — the organization there is different, you see. There are public lectures and there are private lectures. The difference is only that in the public, anybody can register, any student. And in the private, which are more advanced, you have to get the permission of the professor. The private would be what is called here “graduate,” but there was no graduation, except the doctor’s degree. The grades don’t make any difference. In all European universities mathematics is started earlier than in this country. And so there is a difficulty here of getting students of theoretical physics, because by the time they have started asking for independent work, they have not the mathematical background to do work in theoretical physics. They are all pushed into experimental physics as I was in Moscow. But in Munich and Zurich they were pretty well prepared, though I must say that you didn’t have many students in theoretical physics at Zurich. [There was] Zwicky, who was not in the University but in the Technical part. He took courses with me though.
They had the right to register at the University too. But he was essentially a pupil of Weyl so he was a mathematician at that time. No, but that is very strange about — in Zurich he was definitely a mathematician. And that he came at Zurich into physics was just an option. But now as he developed he is definitely not a mathematician, he is an astronomer — a very strange phenomenon! The difference [between German and American schools] was that in all the courses in the German universities, including Zurich — Zurich was also organized like the other German universities the course was in general stiffer. They worked more, they were more advanced when they graduated. They did not require, for instance, from the experimentalist as much mathematics as they do here, but they got it early. In the Dutch university, in Leiden, the difference was that it was the most brilliant group of students that I ever saw, they had really an exceptional sort of training there. I had four students who made a name for themselves: Goudsmit, Uhlenbeck, Dieke, and I can’t think now of the fourth. I was not formally Privatdozent at Leiden. I was assistant to Lorentz, but Ehrenfest took a few months off, and gave his courses to me, so I lectured. Lorentz was then an old man — he came to Leiden just one day a week, so my assistantship was not very ordinary.
In fact my main job was managing the library there. The library of the physics department, and giving these lectures. Apart from that I could work for myself. I gave two courses, one for young students and one for advanced students. The former was five hours a week and the advanced course was four hours. And in addition I had a seminar several times too, but what it was I have forgotten. As for the course for youngsters, I don’t remember everything at the moment, but there must have been altogether eight courses. I remember I gave a course on theory of electromagnetism, and …then I had a course in mechanics with a seminar which was really a problem course. I also had a course in theory of heat radiation. Now one of the courses, a course that Zwicky took, was differential equations of mathematical physics. The seminar for that course was from 6:30 to 8:00 in the morning! It was two hours in succession, but the usual half hour intermission was taken first. Fortunately I did not live far from the University, but there was no time in the schedule for another possibility.
What was the origin of your paper extending the Bohr correspondence principle?
Well, the Bohr correspondence principle of course I learned from Bohr’s papers. But here there was again a formal reason for my writing. You see, I turned in the Stark effect paper as my thesis for getting the Privatdozent. But, since I was a civil prisoner in Munich and couldn’t get away, there was a delay of three years. And they had a rule that this thesis must not be published before I began. So that I had to submit to them a thesis that was not published. And therefore I took that paper and I wrote it in two weeks, the whole thing. With the calculations, everything. And for that reason some of the equations are simplified.
Which paper is that? Is that the one on the Fowler series?...
Ja, that is right. There the calculations are somewhat, simplified. They could be done better. Now, I must tell you that by that time I had already suspected that the whole Bohr theory was not quite the last word. Namely, I worked out the theory, the perturbation theory of the quantum theory, which I later published in both English and German. And I had already made the calculations for the dispersion of the hydrogen atom; I don’t know whether you know that paper, and they didn’t agree with some observational answers. Of course there was always the question whether it was right. But I thought it was probably right, the mathematics, that is. And I doubted the whole theory, and I have here I think an abstract of a paper which I gave orally in the meeting of the Society for the Advancement of Science of. Switzerland.
It probably was in the Archives Néerlandaises for 1919 or 1920. There I said that one should look for a theory, where, in addition to the theory of orbits or states and in addition to the quantum conditions of the material part, also the Bohr frequency relation is included into the foundations of the theory. Ja, I found the correspondence principle an approximation which may be good or not good regarding the calculations. … Well, I can tell you that Bohr’s correspondence principle was received very enthusiastically by us in Munich. At that time Rubinowicz was in Munich also, and he had anticipated some of these things. Incidentally, after this paper of Rubinowicz, I worked out what is, now called the Heisenberg-Pauli theory of the electro-magnetic field, the quantization of the Maxwell equations. The preparatory part is exactly like they did it, the same potentials and so on. I had my own quantum conditions and worked out the quantization. It never was published.
How did Rubinowicz regard the selection rules of Bohr, which were different from his? That is, Rubinowicz gets zero and ± 1, and Bohr just gets ± 1.
Ja. Well, that depends. I think Rubinowicz’ are more correct. You see, according to the correspondence principle, when you have an oscillation which is normal to the direction of the azimuthal, then you can have zero.
Yes, but I was thinking only that to take the possible transitions, one has got to admit more following Rubinowicz than following Bohr.
I do not remember exactly what Rubinowicz said. I think the fact is that Rubinowicz’ is not too detailed. You see this transition, the — 1 and the 0, do not occur at the same time. They occur in different systems. Now Rubinowicz’ is an overall theory which doesn’t specify which electron can occur in a system.
Once one realizes what the quantum numbers stand for, once one realizes which one is the total angular momentum, these rules are easier to apply. When you yourself, in the Stark effect, used the empirical selection rules of Sommerfeld, was there any theoretical consideration at all?
There was not. In the early paper I called it a peasant’s rule of thumb, just because I wanted to use it.
Was that regarded as a particularly important difficulty with the whole Bohr procedure, that one just used these rules of thumb without any justification?
Well, it was regarded as an incompleteness, but it didn’t depreciate the theory — just an incentive to refine it. And I think that in other places it was also received with open arms. In fact, you see, it was over-appreciated, so to say. That is, I thought that it was just another step in the right direction, an approximation, but not the truth. For instance Kramer’s and others tried to formulate it, they tried to take averages over two states by integrating. I told them several times there was something completely wrong with it, that you must include the rule in the foundations. You must have a rigorous formula, not one that has to be integrated. You must depend upon the properties only of the two orbits, not the intermediate ones.
You say in your paper on the Stark effect in the Fowler series that your results, which agree with Stark’s measurements, substantiate the correspondence principle, which you see as narrowing the gap between the quantum physics and classical physics. At this point, were people generally prepared to think that progress should be sought in trying to bring these theories closer together, rather than in requiring deeper modifications of the classical theory?
No, I think they realized that there must be really deep modifications. That was clear from the start. I mean this only in the formal way, that the final representation will automatically derive the relations. No, I never thought that you could maintain the classical theory.
Well, if we could go a little further in this general direction, what were considered the main difficulties or problems still to be solved after the correspondence principle?
Well, of course, the problem was to get a better thing than the correspondence theory, because the correspondence principle does not work back on the levels. The levels are those of the original Bohr theory, and in my opinion these were not correct, so there must be a theory which combined the correspondence and the levels. I think Ehrenfest also realized that the theory should give different expression to the levels and should be a unitary theory, that is unitary in the calculation of the levels and of the intensities. Ehrenfest’s idea was that it must go out from a theory of dispersion. But he didn’t know how, and he worked and he worked and did not get anywhere.
Did you make efforts yourself towards a reformulation of the levels?
No, I never got into that. You see the first year in Pasadena I was finishing up the work I had already done. It was done in a rough way and had to be improved. Besides it had to be written in English and it was in German, and I didn’t know much English. So I worked on that, the theory of perturbation and its application, and I did a lot of work on the theory of the helium atom. I got the same results as Van Vleck did, a good deal earlier than Van Vleck, incidentally. I got this already in Zurich and then I worked further approximations, but it remained essentially the same, the higher approximations didn’t amount to anything. I think that Van Vleck’s method was wrong, but he got the same results.
I’m very much interested in the early attempts to reformulate the Bohr levels and to try to find out which way it would be the most rewarding. Do you know others working on these problems at the same time that Ehrenfest was making his attempts?
No, I don’t know of any. There was something to do in the practical aspects of applications to details of spectroscopy. For instance, the theory of bands, the theory of the Zeeman effect, and so on. You see, I thought the important question was one of principle — to remove the excess of lines at that time. You know that there were more lines than the Bohr theory provided, both in the X-ray and optical spectra. This led ultimately to the spinning electron. I did a good deal of thinking about that, but I didn’t hit on it. My two students found it, Uhlenbeck and Goudsmit. Goudsmit was already a spectroscopist when he came as freshman to the University, for in high school he had a teacher who specialized in spectroscopy.
Can we go back to some of these more fundamental papers you did? You mentioned, when we were talking about your work in 1915 that it was only later that you went back to search the literature for older work on the Jacobi theory.
Oh ja. You see after I got out the first paper on the Stark effect, I got somewhere a reference to Charlier. Now Charlier was not in the Munich library anywhere, and I had some difficulty in buying it even, for some reason it was not very available. But finally I did get it, and I have it even now. And there the theory of conditionally periodic motion was quite well treated, and moreover he mentioned Stackel, whose thesis I could get at the University library. I didn’t know of it before, but I got it, and studied it very carefully. But there isn’t much more in it than Charlier gives. But after that I could understand Schwarzschild, and could show that his method must give the same results as mine, since we used the same conditions. And incidentally, when you use the theory of contact transformations, then it is all included in that. The book of Whittaker, although it had come out, was not available in Germany. I got it only through Ehrenfest from Holland years later. And Whittaker gives in the first edition a theory of approximations that is completely wrong. I wrote in one of my papers that it was not correct, and be omitted it from the following edition.
When did the Hamilton-Jacobi theory enter the curriculum?
Well, I can only say that I started to teach it in Pasadena from the beginning. It was not taught in Germany in 1916 though; things do not happen so fast. It takes a few years. But you see, when I wrote the paper out, and presented a typewritten copy to Sommerfeld, when he saw that it was based on the Jacobi theory, he was furious. He didn’t like Jacobi. Klein, his teacher, had some prejudice against Jacobi, and that stuck in him.
You found a transformation that would let you do the asymmetric top, that had been worked out in the nineteenth century. Was it usual for people to look back at these?
Well you see, a mathematician named (Hilm) told me about it. His work was not very far from Munich, and he often was around. He was interested in this whole business, and I talked to him occasionally about it. And when this paper of Reiche’s appeared, which I referred to, then (Hilm) told me that in addition to the transformation used by Reiche, there was also a contact transformation.
It would be interesting to find out how many of these transformations were already available at the time.
Well you see, for the quantum mechanics you can definitely say that there are no transformations, no point transformations for other coordinates than the elliptical. The elliptical and their degenerations which include the Cartesian circle and so on. But that isn’t true of contact transformations to this day nobody knows which can be done and which can’t. Reiche also didn’t find the transformations which he used. He got it somewhere in the literature. [OVERNIGHT BREAK]
I was listening to the tape a bit yesterday, and some further things occurred to me. So may I ask you one or two more questions, especially about Sommerfeld’s visit to Zurich in 1911? You said his visit there with Einstein is what persuaded him to take the quantum seriously, but there was a paper on the quantum theory published by Debye in 1910.
Do you mean the derivation of Planck’s law? Well, that had certainly an influence on Debye, and to some extent maybe on Sommerfeld also. You see I am not sure that I get all the dates right. This may have been in 1910 already and not in 1911. You see when Debye started on this paper, he got the impression, and he told me so, that he could explain everything by a maximum of energy, not a minimum. So his ideas of quantum theory certainly were very dim at that time. And then after working for quite a while he found out this is not a maximum but a minimum. Really the paper is a little fuzzy, and what it amounts to is really that there are light quanta in the electromagnetic field — the same thing which Schrodinger did many years later, and also Rubinowicz did in his quantization. That’s the right way of doing it, but Debye didn’t do it that way in his quantization of waves.
But it was mostly on his own — Sommerfeld wasn’t interested?
Sommerfeld certainly knew about it, because Debye worked in the next room to him, he was his assistant then.
Then, I have some questions about the two Planck hypotheses, of emission and absorption: One that only emission is discontinuous and the other that both are. You say in your paper in 1919 or so, that it’s one of the most important questions outstanding in quantum theory to decide between these two. I wondered how long this was considered a large problem, if it went all the way through ‘25? ...
Well, it came up only around 1908 I think, or thereabouts. It continued until Bohr was accepted, although not completely. Einstein now accepted it. Very early he believed in the photon — then it was in 1909 probably that he gave his talk at the German Association for the Advancement of Science.
Do you recall whether that talk of Einstein’s had a great effect?
No. You see, the chairman of the meeting was Planck, and he immediately said that it was very interesting but he did not quite agree with it. And the only man who seconded at that meeting was Johannes Stark. You see, it was too far advanced, it was the same thing as the theory of relativity before Minkowski.
Shall we finally come to Pasadena?
Now when I one came here of course, there was no curriculum, so to speak, of the scientific school, which Millikan wanted to establish. It was just a strict institute of technology and engineering. So I decided that the best thing for them would be, to start with, a course in the mathematical technique of theoretical physics; of differential equations and mathematical theory. That was the first course I gave, and I had maybe six listeners, including two professors. But they were quite interested, and it was a successful course. And after that I found they were poorly prepared in mathematics, though I had only graduate students at the time. Their mathematics was extremely fuzzy. It was not so much that they couldn’t handle it, but they were not really confident. That was of course the students from the technical school, but we had from the start a few men from outside, students whom Millikan brought along from Chicago. However, this is largely the fault of the high school here.
They just weren’t doing work in high school and so they have to learn the rudiments of mathematics, which they should know, in the university. And that is the main reason why they become mature in mathematics so late and cannot become theoretical physicists. I had intended to continue my schedule of Zurich, that is two courses in mathematical physics every semester. But it turned out that the students were too overloaded, so that there was only one course. I didn’t complete my cycle of theoretical physics courses because, while, it was possible to cover it in six terms, we imported more and more professors, who all took certain specialties. I was elected to teach candidacy courses, courses the students must take before they are permitted to become candidates in the university. As I say, the mathematical preparation was rather poor but that has improved in as much as our own under-graduates are now very good at Cal. Tech. We take only the best graduates from high school. In general you see, they talk a lot now about exposing the students to more science in the high school, but I think that as far as the university teachers are concerned they should rather have some mathematics.
What they learn of science in the schools is not always the right thing. We have in Moscow incidentally an interesting case. We have these regular examinations every year, as you have also in America, which are unknown in the rest of Europe. Well, one year we had to flunk out two thirds of the students in physics — it was quite appalling. On formal investigation it was found that there was a very popular lecturer in physics in one of the foundations, a very good and persuasive instructor, and that the students who attended these courses of his learned completely fantastic things! Well, what were my relations with Millikan and other experimental physicists at Cal. Tech.? Well, with Millikan my personal relations were very good, and the first year I also collaborated with him. He was interested in the resistance of falling particles. And I wrote a paper on that with him, which was published. There is however one difficulty with a man of Millikan’s ability, and that was that he had too many ideas. I wanted to get people working on some of my ideas, but that was impossible; Millikan had too many of his own, and the men were not available. That was not the difficulty all theoreticians find usually. Because on the other hand when you have younger men, then they take your ideas and appropriate them, and //only give you a footnote//.
What about theoretical physics in the United States at that time in general? Were there many schools that even offered a course?
Well, I don’t think there were many. There were not too many qualified men. … What went under the name of theoretical physics was really mathematics. For instance, Mason was a theoretical physicist, but he was only interested in mathematical problems, not in the physical aspects. And also that man at Yale, who had a textbook out. There were others, but they were also mathematicians. And what really brought physics up were the international Rockefeller fellowships. That was a very important influence on the development of theoretical physics. For instance, Breit was one who came back about the year after I came and he was a thoroughly modern theoretical physicist. And in a short time there was quite a number of others. Oppenheimer was at that time in Europe, and then came out West.
You mentioned your paper on the resistance of spheres. I believe you gave that at an American Physical Society meeting in Cambridge. Also present at that meeting was Darwin, who gave a paper on his dispersion theory. How was that received by yourself and others?
Well, I was not particularly interested. It didn’t make a particular impression at that time. It was a very sound paper, I thought. Ewald’s doctoral thesis had much the same results.
At that meeting, besides yourself and Darwin, Duane and Compton were also present. Do you recall that Compton made any report on his work there?
Well, his work on the Compton effect wasn’t yet done at that time. It was not reported. He came to Pasadena the next year, and then he was in the process of doing it, and talked about it. But of course he wondered then whether it would come out or not. He had done work under Rutherford, with gamma rays. That was what started him out, that the secondary gamma rays were of very much lower energies. So how to explain this result interested him. Well, when the results were obtained, there were not many who doubted — the results were proof of the pudding. Now what I have told you yesterday was the continental point of view, I didn’t know much about England. But you must remember that we were cut off during the war. And so we just did not know about Millikan’s work of 1916 until quite a stretch after the war, because it took a long time to get the journals and to read them and so on. I didn’t know about it until I met Millikan in Holland in the summer of 1921. He told me then about this institute and asked me whether I would like to come for a year. They had on their budget an appropriation for visiting professors from Europe. And when I was there they saw I was a good lecturer, and they asked me to stay on. The second European visitor was Darwin, the third was Lorentz, and then Ehrenfest. Also Sommerfeld came but just for a visit — he was not a lecturer. So I think if we had known about this Millikan work, we would have believed in the photons or light quanta before that, but it only became known shortly before Compton’s work. But of course in England they may have known it and accepted it earlier. During the First World War the separation of the countries was much more complete than during the Second World War.
What about the work you did with Ehrenfest, that started soon after your arrival here?
Oh, that really was a potboiler. The first paper was essentially mine and the second was essentially his. The first was written mostly before he came, and he came out and liked it, and we did a little together, and therefore it was signed “Epstein and Ehrenfest.” The idea for the second he had — I must say I didn’t like it even particularly. Now Ehrenfest had the idea that he was not a mathematician, but in spite of himself, he simply was a mathematician. But he did not like to do calculations so this was up to me. He was not only a mathematician, but also a physicist. And what was remarkable about him was his great dedication he lived physics. That was what impressed me so much about him.
Did you notice any big change in him during the time you knew him?
I knew him quite well, because during my time in Munich he used occasionally to come and to stay with me. His wife was Russian and for that reason he went to Russia, and he came with the intention of settling there. But he found out that for a man that has not the requisite credentials, it was a very complicated and almost impossible rigmarole. He had now to go through endless examinations and so on, so that was simply not feasible. He liked the Russians very much ... but it was no go. So he had to look for a place in Germany, and there of course the beginning was to be a Privatdozent. When he was staying with me in Munich his objective was to look around in German universities. He wanted of course only a good university, but there were no openings. In Berlin Planck told him, “Well I can’t because I have given a promise to Reiche.” And Sommerfeld had no end of his own pupils to place. The only place with an opening was Leipzig University. But back from the 14th century the University of Leipzig doesn’t recognize Vienna and Vienna doesn’t recognize Leipzig. He has a doctor’s degree from Vienna so technically in Leipzig he has no degree, and to get a degree elsewhere, there was residence of three semesters. However, it was for him an interesting trip, because he visited all of the laboratories and traveled over Germany and visited Einstein, but he came back without having anything accomplished in the way of finding a position. But when he came back home he found waiting for him there a letter from Lorentz, who offered him the Leiden chair. He had worked a year under Lorentz in his postgraduate study, and Lorentz was very impressed and had followed his publications. He had just brought out the encyclopedia article, and that, paper on quantum theory.
Can you continue with Ehrenfest?
I should not speak about him personally because he was really a sick man all the time, even from the beginning in Russia, though he had many friends. …But you see he brought into quantum theory the idea of the adiabatic process. He had studied under Boltzmann, and apart from Hasenohrl, he was the only man who knew about the adiabatic transformation. I know that I had never heard of such a thing until his paper came out. It was of tremendous importance for quantum theory — it was an important contribution. It is not as general as people think it is, and Ehrenfest and Burgers themselves. You see, it holds only as long as the system remains conditionally periodic, but there are degenerations as you go from one position to another continuously. I mentioned it in my article in the Gibbs Memorial volume, the Gibbs Memorial Publication in two volumes. The first volume was about Gibbs on physics, and the second chemistry. And in the Gibbs on physics, I wrote three articles: first about Gibbs’ thermodynamics, which I later expanded into my book; and second on statistical mechanics, not a review of Gibbs, but an independent presentation like Ehrenfest’s. And third there was the thermodynamics and the quantum theory.
During this time it seems to me you get involved in something new for a little while. You published a paper on paramagnetism.
Ja, well, that paper of mine was not quite right. You see, my method of approach was a good one, but I forgot //about a transformation which could be used in addition to those there employed.// When it is included the results are different.
Was that a subject for research at Cal. Tech.? Were people interested in measuring experimentally the paramagnetism of various materials?
In a minor way. You see, when I came here there was a man here, whose name I think was (Williams), who was interested in… And I was interested at that time already in the theory of paramagnetism to some extent. Maxwell’s theory of paramagnetism, in the Treatise, was the realignment of complexes, which we call today domains. So I was interested in the nature of these domains, how they reorient and so forth.
Most of that work was done in Spain, wasn’t it?
Yes, Cabrerra had done work on liquids. That was another point that entered, you see. Cabrerra applied Weiss formula and found magnetons which were about 1/5 of the Bohr magneton. I pointed out that if one takes the quantum formula you come out right. … Well, at least I thought it would come out so, and I was not mistaken.
We have come to the new quantum theory, to its reception at Cal. Tech. and elsewhere. I’m interested in the first place that, as far as I know, you didn’t do anything on the matrix mechanics but that people at Cal. Tech. were very quick to do things with the Schrödinger mechanics.
Well you see, we accepted [the matrix mechanics] with open arms. As I told you yesterday, I was not satisfied with the Bohr theory nor was Ehrenfest either. He thought that everything would come out of an analysis of dispersion. I also had this paper on dispersion and so on, so that the matrix theory //hit us favorably//. … When this thing came out Ehrenfest wrote a letter to Heisenberg saying, “What an idiot I was that I never thought of that,” And. I also saw at once that this was the solution. But matrix mechanics was very cumbersome and I never worked in it, because in Gottingen there was Born, Heisenberg, Pauli altogether, so I thought, leave it to them. They were really a tight group and worked together, and you know the effect goes quadratically when people work together — so a single man had no chance. Well, as a matter of fact, Schrodinger did not come from this track. He came from another track. As he told it to me later, he had read de Broglie carefully. Here I am a little guilty myself that I did not study sufficiently this paper of de Broglie’s, for when de Broglie’s paper came out, I gave the study of it to a student to report in our seminar. That student, though an able fellow, was just completely at sea with it. You got the impression that it was just nonsense.
Incidentally, Ehrenfest was in Pasadena that year and he attended the seminar and he told me “That’s what comes out whenever a ‘goy’ does physics.” And yet I gave it a second time here — Eckart talked about it. He may have understood it because he had studied it earlier, but from his report one couldn’t make heads or tails out of it. However Schrodinger studied it thoroughly and had a good idea what it was. Then when Einstein’s paper came out on the Einstein-Bose statistics, where he expresses a high opinion of de Broglie’s thesis, Schrodinger decided to go into it thoroughly and especially to work it out three-dimensionally — de Broglie’s approach was essentially one-dimensional. And this posed the question how to represent these waves which led to the fundamental equation of Schrödinger’s mechanics. But he was not sufficiently a mathematician to make use of it; his idea of doing the hydrogen atom was to make the waves vanish at the surface of the sphere. Only by dint of studying Courant he found out that conditions at infinity play an essential role and then he had it. Now I knew the theory of differential equations and there was nothing new for me in Courant-Hilbert, but he did not realize that conditions at infinity entered. … Later Schrodinger [perhaps with help of a letter from Pauli] showed that his mechanics was mathematically equivalent to Heisenberg’s.
Work on that was done at Cal. Tech. too.
Well at Cal. Tech., Eckart was more interested than I, and, when this first paper came out, he tried to apply it to different things. But I wasn’t particularly interested in the easy problems, so I took the Stark effect. You see, Eckart had some previous mathematical courses in Princeton where he learned the operational calculus, and the commutation laws of momentum and coordinate were quite familiar to him already.
So he brought the interest and the apparatus with him.
He brought the apparatus and the knowledge of de Broglie’s paper; the interest was at Cal. Tech. anyway.
You say you put students earlier on to reporting about de Broglie’s paper. What made you look at it in the first place? Did you ordinary look at the Annales de Physique?
I looked at all journals. You see, I was really isolated here. In Moscow and in Munich you could rely on your friends to point out things of interest you may have missed. But that was not possible here. I was alone from the beginning. In Moscow the colloquium was run like this: the members // of the colloquium would report on papers and give a general idea of the content, and one could then pursue the matter further on one’s own.// This worked out fine because everybody had heard the preceding papers for the year, and this gave one an historical introduction to a subject.
In your work on the Stark effect, which you did in 1926, you got results which differ in the second order from your 1916 paper. From some measurements on the second order Stark effect made in Japan you concluded, in an article published in Science in 1926, that although the new theory gives slightly better results, it is not yet conclusive. Was that just an excess of caution or were you still unconvinced?
No, I was not unconvinced. You see, what I wanted was to have a clear case to convince others. In other cases the differences with the old theory were not quite definite. It was not known how to apply it, or there were other difficulties. Here the predictions were clear and led to results that were different. They showed that the new theory had a conclusive advantage.
I’d like to know how this paper in the Amsterdam Proceedings was received — the paper in which you correct your earlier work on hyperbolic orbits, which wasn’t very well-received.
I think it was received with interest but not much more than that. It was not a very important paper, you see, because it only introduces a discontinuous spectrum in a way this was a new idea but there was no direct way of checking it. I do remember it caught the attention of Rutherford, and he said something about it, but I don’t remember what.
But I think you say there that you can account for various measurements made by Rutherford already and you predict some new ones which Rutherford indicated he had found already.
Well, I’ll read this paper over and we’ll talk about it next time.