Hans Bethe

Hoddeson:

This is Lillian Hoddeson. I'm speaking with Hans Bethe in a very lovely room at the top of a tower, at the International School of Physics Ettorre Majorana in Erice, Sicily. The date is 29th April 1981. The theme of this discussion is solid state physics circa 1933, but we will begin about 1928 and move up somewhat beyond 1933. Fortunately much of the background has already been done for this interview, part of it in your earlier long interview with Dr. Charles Weiner, which was carried out in 1966-67, and in various talks you've recently given on your life as a physicist, one version of which I was fortunate enough to listen to a couple of nights ago. (Copy of tape available from Lillian Hoddeson in Urbana to be deposited at AIP in 1984.) So we will be able to build on that, since anybody who uses this interview will have access to that material. We'll be going back and forth between your work in solid state physics and the general environment in which you did the work and I'll be asking you also to act as an observer of what was happening around you. I don't know whether the starting point is your thesis work and the follow-up paper on electron scattering in crystals, or Sommerfeld's seminar. I don't know which of the two happened first, or whether they happened simultaneously.

Bethe:

Well, the thesis and Sommerfeld's seminar happened simultaneously, but maybe I shall start with Sommerfeld's seminar, which was really a series of regular lectures, a regular course in advanced quantum mechanics announced for his advanced graduate students. This was in 1927. Just preceding that course, Pauli had published a paper on the paramagnetism of alkali metals, in which he showed that you could explain the rather weak magnetism of alkali metals on the basis of electron theory, if only you assumed Fermi statistics for the electrons. So Sommerfeld saw this, and wanted to go back to problems which intrigued him 20 years earlier.
Twenty years earlier, Drude, a German physicist, tried to develop a theory of metals on the basis of electron theory, and of course everything turned out wrong. Most important in the older theory was the specific heat of the metal. If there were electrons in the metal and they obeyed classical statistics, then you would have to count the electrons as separate particles, and so instead of having a specific heat of three times the Boltzmann Constant, you would have three plus 1 1/2 times the Boltzmann Constant — three for the atoms vibrating around fixed points, and 1 1/2 for the electrons which were supposed to move freely. Of course, there were many appealing parts in the Drude theory as well. You could explain the electric conductivity. You could explain in Drude's theory the ratio of thermal to electric conductivity, the Wiedemann-Franz law. That had a coefficient 3 in the older theory, which agreed pretty well with experiment. You couldn't explain the conductivity quantitatively, but at least you could see that it should be there.
So Sommerfeld took this up again, now with quantized electrons, with the Fermi statistics, and sure enough, the specific heat of the electrons became essentially zero, namely, it was kT divided by the Fermi energy. The Fermi energy could be estimated very easily to be equivalent to a temperature of a few electron volts, and so kT divided by the Fermi energy is about 1 percent. And so the electrons would have their specific heat reduced to 1 percent of the classical value. That is not observable at room temperature. You couldn't measure the specific heat with that accuracy. It is observable when you go to very low temperatures, because at very low temperatures, the specific heat of the lattice goes to zero as the cube of the temperature, while the specific heat of the electrons goes to zero only linearly with the temperature. So if you go to low enough temperatures, below the Debye temperature, then at some point you can see the specific heat of the electrons.
Sommerfeld didn't know that, and in fact these measurements were only done probably in the sixties; so nowadays, people have observed the specific heat of the Fermi type electrons quite nicely. Sommerfeld was only interested in showing that the specific heat is very small compared to the lattice specific heat at room temperature. Is that clear?

Hoddeson:

I have a question. You suggested that Sommerfeld had been worrying about these problems for twenty years. There exists some correspondence between him and Drude as well as Lorentz around the turn of the century in the quantum physics history archives.

Bethe:

I would imagine so. Drude I think was more elaborate and more specific, but Lorentz was very unhappy that electron theory didn't work in this case.

Hoddeson:

So it seems that Sommerfeld's having worried about this for so many years may be one explanation for why he was the one to seize upon the results of Pauli's. As I recall, Pauli wasn't primarily interested in paramagnetism but rather in testing which of the two quantum statistics was valid in this context.

Bethe:

Yes. You are absolutely right. Sommerfeld took hold of it exactly because it had occupied his mind for 20 years, and it was one of the unsolved problems. And so here was a possibility of solving it.

Hoddeson:

Was this characteristic of Sommerfeld, to have a problem stick in his mind for many years?

Bethe:

Yes, it was. I must say, I have somewhat the same attitude. There are some problems which just are insoluble at one time, and you store them somewhere in your memory, and maybe ten years later, the method is there to solve them. I think that's a very good way to proceed. Pauli, as you said, was really not interested in the solid state at all. You probably know the story — I think it was in '33 or so — Pauli wanted to have an assistant, and he thought of me and of Weisskopf. And he decided, "No, I don't want Bethe because he does solid state theory and I'm not interested in that at all."

Hoddeson:

I hadn't heard that version. I heard a different one from Weisskopf.

Bethe:

The Weisskopf version came later, and they belong together.

Hoddeson:

To go back to Sommerfeld's lecture course and also the seminar, Sommerfeld had been teaching some solid state physics in his courses, hadn't he, even before this?

Bethe:

I am not aware of it. When he did this work, I had been with Sommerfeld for one year. During that year, he had not taught it. But that is connected with the peculiar German system of theoretical physics lectures of that time, which in fact persisted still after the war, namely, Sommerfeld gave a cycle of lectures which carried through three years, six semesters, starting with classical mechanics and mechanics of continuous bodies, hydrodynamics, then thermodynamics and statistical mechanics, then electrodynamics, then optics, and finally mathematical physics, in particular the theory of partial differential equations. These were six successive one- semester courses. The most beautiful of them in Sommerfeld's case was the last one, on mathematical physics, but also his optics was very good. This was imitated by lots of other theoretical physicists all around Germany. I don't know, it may have developed even before Sommerfeld. I know that Heisenberg, even after the war, went through the same cycle, which at that time really made very little sense. Sommerfeld, as I made clear in my lecture the other night, was very much devoted to quantum mechanics, but there was no semester in that long cycle devoted to quantum mechanics.

Hoddeson:

Who was the quantum mechanics given by?

Bethe:

That was given by the Assistant, and of course Assistant really meant Assistant Professor. There was an Assistant Professor. He gave a quantum mechanics course which took only one semester, and it came every two years or so. It was most remarkable that it was treated so briefly. And when I became a Privatdozent I gave a course on collision theory, since that was what I knew. I don't remember what the distribution of courses was otherwise. There was normally this big course given by Sommerfeld. Then about every second semester, he taught a small course on a very advanced subject such as the theory of solids. The Assistant Professor taught a course every semester, and those courses were mostly on quantum mechanics.

Hoddeson:

About how many students were in the large lecture course?

Bethe:

About a hundred. And in the small courses, about 20.

Hoddeson:

And the seminar was still smaller?

Bethe:

No, the seminar was also about 20, because the seminar included all the American visitors.

Hoddeson:

You mentioned a few of them the other night. They included Condon and Rabi. And I gather Pauling was there?

Bethe:

Pauling was there, I believe for one year.

Hoddeson:

And Lloyd Smith.

Bethe:

Yes.

Hoddeson:

And then Houston and Eckart were other Americans.

Bethe:

Yes.

Hoddeson:

Now, I don't know if there were any more Americans, but we have to mention the Germans as well. There was Peierls....

Bethe:

No, stick with the Americans, first. I mentioned Kirkwood, and he was very important. He became as probably you know, a very high class physical chemist. Once I returned from England, by the way, it was my job to keep the visiting Americans busy. Since I knew English, I was detailed to give problems to the visiting Americans, and that's how I got to know Lloyd Smith and Kirkwood very well. I asked Kirkwood to try and do some work on solid parahydrogen. I don't remember whether he actually published this. It was quite a nice paper.

Hoddeson:

This is now two years later, roughly. You were in England in 1930, I believe?

Bethe:

Well, it went this way, to be accurate. In the fall of 1930, I went to England. Then immediately afterwards, I went to Italy to Fermi, and returned in the summer. (Notices biographical file on table.) Oh, that's all here, so I don't need to repeat it.

Hoddeson:

Probably not. In the seminar at the moment we're talking about I think 1928?

Bethe:

Yes. But we got diverted to the American visitors. I was talking about American visitors during the entire time.

Hoddeson:

Spanning all the way up until about when?

Bethe:

Until I left in the fall of '33.

Hoddeson:

Who else was influenced by Sommerfeld's extreme enthusiasm about the new electron theory of metals he was developing?

Bethe:

Houston, very much. Eckart, I don't believe quite so much.

Hoddeson:

Eckart did write a paper either on the Richardson effect or some small extension of Sommerfeld's main papers. It concerned contact potential at interface between two metals. [C. Eckart, ZS. f. Phys. 47 (1928) 38.]

Bethe:

I don't remember.

Hoddeson:

What about Peierls?

Bethe:

Now, Peierls was a graduate student. He was a year younger than I. He just studied at that time and went to the lectures and to the seminar, but he did not yet start a thesis. He did his thesis afterwards, with Heisenberg I believe.

Hoddeson:

I don't remember now.

Bethe:

I'm pretty sure it was with Heisenberg. And then he went to be Pauli's Assistant.

Hoddeson:

I gather he went back and forth; they somehow exchanged him.

Bethe:

I think he did. Yes. But his big papers about solid state physics came after he left Sommerfeld.

Hoddeson:

Right. Was there anybody else in that seminar that we've left out, who then went on to work in the area under Sommerfeld's influence?

Bethe:

I don't remember, and I think Sommerfeld himself stopped working on it pretty soon after. I don't believe he continued after 1930. But I may be wrong.

Hoddeson:

I think you're right. I think he then went in another direction, though for a good part of that time he spread the gospel in many places.

Bethe:

Yes, indeed.

Hoddeson:

In Japan I heard stories about Sommerfeld's lectures there in the winter of 1928.

Bethe:

Yes, well, of course he went around the world and surely he would talk about that subject.

Hoddeson:

And he got many people interested in it.

Bethe:

Yes. It was really quite remarkable, how everything turned out right which had turned out wrong previously. With one exception: that was the Hall effect? The Hall effect, you know what it is — didn't come out right because Sommerfeld knew only about free electrons, and in order to understand the Hall effect, you have to take into account filled bands and some few vacancies which act as positive charges. We talked about that I think the other evening. I'm not sure, but I believe that this was the first connection in which the defects, the missing electrons, were taken really seriously. That is, the fact that they had effectively a positive charge.

Hoddeson:

I think that's right, and that appears in the Peierls paper in 1929. R. E. Peierls [Zeit. für Physik 53 (1929) 255].

Bethe:

Right.

Hoddeson:

There were also some other problems with Sommerfeld's theory, which, I gather, disturbed you, already in the seminar.

Bethe:

It disturbed me that he considered the electrons as completely free. How could electrons be completely free, when there are all the ions sitting around attracting them? And that was only solved by the Wigner-Seitz paper.

Hoddeson:

Well, Bloch then made a contribution.

Bethe:

Yes. I was wrong! Bloch took the most important step, namely, by showing that even in spite of a strong periodic potential, these electrons would move completely freely. I think that was the most important step.

Hoddeson:

Before we move on, I want to ask a very general question about Munich. This seems to have been the major center for solid state physics at that time in Germany, although certain other centers, for example, Berlin, was important to a certain extent.

Bethe:

Yes, to solid state theory, that is —

Hoddeson:

Yes, because — well, Born.

Bethe:

Born was in Göttingen. There were experimental physicists in Berlin in large numbers, I think, Grüneisen and ...

Hoddeson:

He was in Berlin?

Bethe:

In Berlin. But I don't know very much about him. On the theory, well, Sommerfeld's school was first, but then, you see, Bloch and Peierls both were given theses in solid state physics. And both did spectacular work, really better than anything that came out of Sommerfeld's place.

Hoddeson:

But that was a year or two later.

Bethe:

It was a year or two later.

Hoddeson:

And then Leipzig. But only because Heisenberg had moved to Leipzig.

Bethe:

Heisenberg was terribly interested — yes. Of course he did ferromagnetism, and he stimulated these theses.

Hoddeson:

But Munich was also a place where some 12 or so years earlier, there had been the major development in X-ray crystal diffraction.

Bethe:

Yes.

Hoddeson:

Historians always like to ask, why did certain things happen where they did and when they did. The question is really, what was so special about Munich? Maybe it was just Sommerfeld

Bethe:

About Munich? Sommerfeld! Now, I don't know the early history of Laue's discovery, whether Sommerfeld played any part in that.

Hoddeson:

According to your father-in-law, Ewald, the experiments were done despite Sommerfeld at first, at night. That's in his book. [P. P. Ewald, "The Beginnings," Fifty Years of X-ray Diffraction (Utrecht, 1962) pp.6-80.]

Bethe:

Beautiful. Ewald is the only person still alive who knows.

Hoddeson:

Apparently after the experiments were successful, Sommerfeld was very pleased and then gave talks on it, and was very proud that it happened in his institute.

Bethe:

Yes. But that means then that it was not Sommerfeld.

Hoddeson:

Apparently Wien thought — I hope I'm remembering this correctly, I read it quite a number of years ago — I think it was Wien who believed that thermal vibrations would upset the pattern.

Bethe:

Oh, yes, right.

Hoddeson:

And so they did not want to support the experiments, but somehow von Laue got together with Knipping and Friedrich, who had the proper apparatus, and convinced them to do the experiment in the basement.

Bethe:

Yes. Well, I'm sure this is very well described in Ewald's book yes.

Hoddeson:

It's a wonderful story.

Bethe:

When I was there in Munich, one of the features of the basement of Sommerfeld's Institute was the jack of all trades, whose name was Selmayer. He was really a machinist, but he also made models of crystal structures as they were discovered, and put together these using little balls with wires between them, strong wires. And those he sold to everybody who wanted them, and we were always convinced that he had a better income than Sommerfeld. And certainly the Selmayer crystal models were used all over the country.

Hoddeson:

I gather then there was a continuing tradition of crystallography in Munich.

Bethe:

Of crystallography — yes and no. I think only in the person of Selmayer. I don't believe that Sommerfeld or any of his normal collaborators did anything about crystallography, between Ewald and my thesis, or Sommerfeld's theory of metals. The interest of Sommerfeld in between was almost entirely the old quantum theory and specifically, the theory of complex spectra. There were great papers about that, Sommerfeld's own papers and those of his students.

Hoddeson:

Yes, and that of course led directly into quantum mechanics.

Bethe:

Right.

Hoddeson:

I think I forgot to ask you before, how often Sommerfeld's seminar would meet?

Bethe:

Once a week.

Hoddeson:

Once a week, and the lectures met — ?

Bethe:

His big lectures I believe met three times a week.

Hoddeson:

For about an hour?

Bethe:

For an hour. The seminar was at least an hour and a half. The small lectures, Sommerfeld's theory of metals, that was twice a week, and so were most of the lectures by the assistant professor.

Hoddeson:

I see. One other question about the seminar. I'm interested in the way it was organized. Did Sommerfeld, in the beginning of the semester, say "OK, you take this subject, you take that subject."?

Bethe:

That's how it was done. The first semester when I was there, and we discussed Schrödinger's papers, Sommerfeld started out saying, "Wave mechanics is the solution of our troubles. We'll discuss wave mechanics, and we'll discuss these papers in succession." The senior graduate student was Unsöld ld, of whom you may know from that awful paper in German. You know that?

Hoddeson:

I haven't read it, but I've heard about it.

Bethe:

But he's a very reputable astrophysicist. He was doing a thesis at that time, and he already prepared a seminar on the first of Schrödinger's papers, and then the others were gradually distributed.

Hoddeson:

What about when the seminar moved up to electron theory?

Bethe:

Well, that was really not the seminar. That was a regularly announced special topics course announced by Sommerfeld, and it was called I think "Special Topics in Quantum Theory" or something like that. These were simply lectures by Sommerfeld. It was not a seminar.

Hoddeson:

I see. Now, when Sommerfeld went on his trip, and you moved to Frankfurt and then to Stuttgart, and Bloch moved to Leipzig along with Heisenberg—

Bethe:

Bloch was never in Munich.

Hoddeson:

Oh sorry. Yes, he started right away in Leipzig with Heisenberg.

Bethe:

Yes. But Peierls moved.

Hoddeson:

—moved to Leipzig, at first. Then Leipzig became the main center—

Bethe:

Yes.

Hoddeson:

—for a while and, I gather, attracted many visitors. People like Slater passed through, and Landau and many others.

Bethe:

Yes.

Hoddeson:

I was wondering whether you spent any time there as a visitor?

Bethe:

No, I never did. I only went to a meeting once, which was arranged jointly by Heisenberg and Debye. It was in early 1933. About magnetism.

Hoddeson:

I see. That would be interesting to hear about. I hadn't heard of that.

Bethe:

Well, I don't remember a great deal about it. I think these papers were written up, but I'm not sure.

Hoddeson:

As a symposium proceedings?

Bethe:

It was a symposium, and I think probably the papers were published in Annalen der Physik. But as I said, I'm not sure.

Hoddeson:

That gives me something to look for.

Bethe:

You might look for it. Heisenberg gave a paper and Peierls and Kramers and I and at least half a dozen other people.

Hoddeson:

Now, we're skipping to '33 just for this little tidbit. By that time, was the main subject of interest in magnetism ferromagnetism? The people you mentioned all did something on ferromagnetism?

Bethe:

Yes. I think the main subject was ferromagnetism. there were some papers on paramagnetism, such as the oxygen molecule. But it was mostly the question, how did ferromagnetism actually come about. It was Heisenberg's theory, and then Bloch had done a paper.

Hoddeson:

—a paper in '29—

Bethe:

—how to get it from free electrons. I don't know what I contributed, if anything. Now, I did give a paper, but I'm not sure just what it was about. One of the worries that people had in the Heisenberg theory was how could the exchange integral have the opposite sign of what it had in, let's say, the hydrogen molecule? In the hydrogen molecule, the exchange integral between the electrons is such that anti-parallel spins have the lower energy. And now Heisenberg wanted the exchange integral to have the opposite sign, so that parallel spins had the lower energy. I remember, that was a problem which I found intriguing. How could that be? I believe I tried to calculate some exchange energy as the function of distance between the atoms, and that's probably what I talked about. At least, that was the main problem on my mind. And of course, only much later did people understand this.

Hoddeson:

You had done a little bit of earlier work while you were in Italy that I haven't yet studied and know just a little bit about, on the linear chain.

Bethe:

You are quite right, and perhaps that's what I talked about. There was another problem besides the one I mentioned, namely, how does ferromagnetism depend on temperature? And I thought one should really go about it by starting from the basics, namely individual atoms having spin, and where the spin can move. There was the Ising model. That was known at the time.

Hoddeson:

That was about 1925.

Bethe:

Is it that old?

Hoddeson:

I may be off by a year or two.

Bethe:

Yes. Well, even if it was old, it was discussed very much at that time still. But it clearly was not the right model, because the spin is a quantum object and not a classical object, so you couldn't just say up spin and down spin, but had to permit them to change direction. And that was the purpose of my paper written in Italy. [Z. Phys. 71, (1931) 205.] I wanted to see, in quantum mechanics, how you could have a chain of spinning atoms, and what would be the quantum states of such a chain. Then I only did it for a linear chain and never thought of it any more. And just before I left Cornell, I heard a talk—and I forget who gave the talk.

Hoddeson:

This is very recent, a few months ago?

Bethe:

Yes. February or so—that people have now found certain crystals which contain one atom with an incomplete shell, nickel in this case, and two atoms without incomplete shells—I think it is nickel aluminum flouride. The nickel atoms are sufficiently far apart so they don't interact with each other, and they are arranged in linear chains. So this is a beautiful example of my old theory. In fact, the old theory was applied to it and it seems to work all right.

Hoddeson:

That's nice.

Bethe:

I wish I could remember names. I can't, but if you ask somebody at Cornell, then you will find out who gave that colloquium.

Hoddeson:

Now, before we go to Frankfurt and Stuttgart, let's go back and consider your thesis work, [H. Bethe, Ann. Phys. 87, (1928) 55-129]. But we don't have to go into that in great detail, because you covered it quite well in your talk the other night. [Bethe, "My Life in Physics," Erice, April 1981. Available at AIP.] I have only one question about it. You mentioned that several other people also solved the same problem.

Bethe:

Yes.

Hoddeson:

Were these people at different centers in Germany, or were they all over the world?

Bethe:

All over the world, and I think the majority were in America.

Hoddeson:

I see.

Bethe:

One I knew about was Patterson, who was a well known crystallographer. You can find the list of all these people in the book that Jeremy Bernstein wrote about me. He describes that particular paper, and he mentions some of the people. And he also mentions the source where he had that from. There was an article about it in Physics Today, I believe, which mentioned all the people—in fact, it didn't mention me. You see, this was less interest in solid state physics than in the Davisson-Germer experiment. The Davisson-Germer experiment was terribly exciting, because just at the same time, essentially at the same time as Schrödinger's papers came out, there was an experiment proving right away that wave mechanics was right. And so, this was exciting to nearly everybody.

Hoddeson:

Did Davisson and Germer respond to your work at all? Did you send them a copy?

Bethe:

I'm sure I sent them a copy. I'm sure that I don't remember any response. But when I had my traveling Rockefeller Fellowship, it was Sommerfeld's idea that I should spend half the year with Davisson and Germer at Bell Labs. And so I think Sommerfeld wrote a letter to Davisson, would he like that? And Davisson wrote back, "Well, if you think he ought to come, let him come." It was not greatly encouraging, whereas Fowler in Cambridge and Fermi responded immediately and very warmly. And I wasn't terrible interested in going.

Hoddeson:

You didn't want to go to America.

Bethe:

That's right.

Hoddeson:

I think you mentioned that the other night also. A question about Ewald. Did he show an interest in your thesis?

Bethe:

Yes, he immediately had an interest in my thesis. In fact, while my thesis was still being written and not completed, he had heard about it, and asked me to come to a little conference he had arranged in Stuttgart. I'm not sure whether it was perhaps a sectional meeting of the German Physical Society; I suspect it probably was. He invited me to come there and give a talk about my thesis, while that was still being written. So I came, and in fact, he invited me to stay at his house. And I gave my talk and apparently it pleased him. So that was our first acquaintance.

Hoddeson:

A direct connection there.

Bethe:

Yes.

Hoddeson:

Do you recall any other strong responses—perhaps some with not quite as much impact on your personal life? How about Born?

Bethe:

Born responded to my other paper, the one about collision theory. He wrote me a very nice letter, and I answered that letter, and only about two months ago, I found out that my answer offended Born. Born understood my answer as saying, "You are stupid that you didn't see this transformation yourself." I am sure I did not mean that. But I am told Born was terrible sensitive, and probably read something into my letter which I hadn't intended at all. Born's response to the second paper and the Ewald response to the first paper, are the only ones I recall. Of course the second paper, which is not our subject today, the one on collision theory, was very enthusiastically received in Cambridge by the people who measured the energy of nuclear particles like alpha particles, by means of measuring their range in air. Blackett in particular thought my theory should be much more exploited than I had done, and I should calculate the range energy relation. And I did.

Hoddeson:

You did that. And was the relation of your thesis to the paper in the Annalen der Physik?

Bethe:

That is my thesis, I think essentially in its entirety. Maybe I left out some of the more messy second approximations. I think I probably did that.

Hoddeson:

Already in this paper one sees your characteristic style of including tables of numbers and making theories that try to take into account these empirical results.

Bethe:

Yes. I wanted to have the connection to experiments. Theoretical physics is rather meaningless unless you can explain some experiments, and if possible also suggest some experiments.

Hoddeson:

But I gather this was not so much the style in Germany at the time. I'm taking this from comments you made in your interview with Charles Weiner, in which you were talking about how you felt when you got to England, after 1933. You commented that there was a need for people to do the calculations and to interact with the experimenters.

Bethe:

With the experimenters, yes.

Hoddeson:

And for some reason those who were theorists in England at that time weren't doing that, people like Dirac. They came out of a more mathematical tradition.

Bethe:

That is correct, yes.

Hoddeson:

And so you actually had a big impact on British physics at that time, you and Peierls and others who came at that time.

Bethe:

Yes, right.

Hoddeson:

And apparently this was not something that you were doing so much in Germany.

Bethe:

I didn't interact very much with the experimenters except in Tübingen. In Tübingen the experiments seemed to be very eager to learn theory and have theoretical suggestions. In Munich, Wien didn't seem interested. Now, I might have interacted and probably should have interacted more with Gerlach, who was Wien's successor, and who was certainly very friendly to theorists, but I don't remember having had any interaction with him on the relation between theory and experiment. It's interesting. And I had not realized this until you brought it up.

Hoddeson:

I learned it from your words in an earlier interview. This also brings up another question for me. In America, in this period of the early thirties, I've noticed that in certain industrial institutions, in particular Bell Labs but also GE and Westinghouse, the experimentalists began to realize that they didn't fully understand what they were observing and that they were missing something that theorists knew. And therefore people like Walter Brattain, who was at that time studying the copper oxide rectifier at Bell Labs, went to hear Sommerfeld's lectures at the Michigan Summer School in order to be able to calculate the work function.

Bethe:

Oh, that's fascinating.

Hoddeson:

That indicates that certain needs were being felt by the practical people in America, needs which would soon be met by the new theories that were being developed. But one would think that something like that would have gone on too in Germany, because there was even an earlier tradition for research in industry there than in America.

Bethe:

There was.

Hoddeson:

But I don't know whether in Germany there were connections of the kind I've mentioned in America.

Bethe:

The only industrial lab that I ever visited in Germany was in Ludwigshafen, which was the Badische Anilin und Soda Fabrik, which had a small research group under Herman Mark. They were studying electron diffraction, which was quite new. The chemical factory was interested in this, to find new ways of determining the structure of molecules. In fact this was the purpose of Mark in having his experimental establishment. He asked me one day to come and talk to them and explain to them how one could derive the structure of a molecule from electron diffraction. They wanted to know the form factor which I had obtained in my thesis, and they had already nice pictures of I think something like CC14, which is of course a wonderful molecule to get electron diffraction.

Hoddeson:

This is about 1929 or so?

Bethe:

Yes. That's the only industrial application in which I was involved. There was a very respectable research lab at AEG in Berlin, the Allgemeine Elektrizitäts Gesellschaft, where the main physicist was Ramsauer and he did his experiments on the Ramsauer effect in this industrial laboratory. So this did exist. I don't know what connection Ramsauer expected between his effect and anything that could interest the AEG. But, anyway, he was allowed to do these experiments.

Hoddeson:

Were there connections between the new work that was going on in solid state physics at some of the universities, in particular Munich and Leipzig, and the work in industrial laboratories in Germany?

Bethe:

I don't think so. Places like Siemens and AEG ought to have paid attention, but I am not aware of it.

Hoddeson:

That's interesting.

Bethe:

Yes. Now, Bell Labs, I think, was much more aware of things going on in physics. Bell Labs of course had K.K. Darrow to explain quantum theory to the rest of the laboratory. I don't think he knew very much of it himself, but he was retained by them for this purpose.

Hoddeson:

He was a good science writer.

Bethe:

He was, yes. And so, Bell Labs somehow had seen the light and saw that there were possible applications of solid state theory. I don't know whether Wigner or Seitz—Seitz I think was at one time—

Hoddeson:

Seitz was at GE.

Bethe:

At GE?

Hoddeson:

For a while. And Wigner gave a talk at Bell Labs that I came across as an announcement in the Bell Labs Record, on the application of quantum mechanics to chemistry, but quite early. It was I think '33 or even '32.

Bethe:

I see, yes. Rose

Bethe:

Bozorth.

Hoddeson:

Bozorth was very active at Bell Labs in paramagnetism. I think Bozorth was one of the early people at Bell who saw the need for quantum mechanics.

Bethe:

Very good. Yes. It's true. But he was an experimenter, rather than a theorist.

Hoddeson:

Well, let's move on to Stuttgart.

Bethe:

In this connection I'm sure I may have mentioned to you already that Kennard who was the senior theoretical physicist at Cornell, maintained all the time that solid state theory could not possibly have any practical application.

Hoddeson:

Really? I don't know how he could have sustained that view!

Bethe:

There were Lloyd Smith and I and Kirkwood, all of whom said that, yes, it will have applications. But Kennard just stuck to his guns and said, "No, this is just pure theory. It will never be applied."

Hoddeson:

Amazing! You began your group theory work in Frankfurt, and I think you mentioned the other night that it was Madelung who suggested that you learn group theory.

Bethe:

No, Madelung didn't suggest anything. He suggested that I should paint in India ink some wiggles on paper which one could then use as a grating and Fourier analyze light going through it. It couldn't have worked. It didn't work. And the other thing Madelung was interested in was the different interpretation of Dirac's equation. In fact he wrote a couple of papers about it, and he talked to me about it. It didn't seem to me then and it doesn't seem to me now that it added anything to Dirac's equation. So I was entirely on my own. But I wanted to understand the papers by Wigner and von Neumann.

Hoddeson:

On spectra; or on group theory applied to spectra?

Bethe:

On spectra. Yes.

Hoddeson:

I see. So you came across those essentially by yourself.

Bethe:

By myself.

Hoddeson:

And decided to work throughout them, because you realized that the theory would be very important.

Bethe:

Right.

Hoddeson:

At that time, besides Wigner and von Neumann and also a certain amount of work by Weyl, was there anybody else?

Bethe:

Weyl I could never understand.

Hoddeson:

But he wrote some papers on that subject.

Bethe:

He wrote lots of papers on it.

Hoddeson:

Was anybody else interested in group theory?

Bethe:

Many physicists learned group theory at the time because these papers obviously were very important.

Hoddeson:

Had anybody yet applied it to solids?

Bethe:

In a way, this application was very old, because long before even the Laue experiment people applied group theory to discuss what possible arrangements atoms could have in a solid. They discovered 32 groups of symmetry.

Hoddeson:

By the way, do you know when that was discovered? I've been trying to find out when that was discovered, and by whom, and haven't yet gotten the answer. [The discovery was by J. Chr. F. Hessel in 1830. See note 1 in W. Voigt, Lehrbuch der Krystallphysik (Leipzig, Teubner, 1810) p. 37. LH]

Bethe:

Well, the final answer of the 230 groups I think was found by Schönfliess and this was probably not very long before the Laue discovery, early in the 1900's. [The existence of 230 space groups was established first by Fedorov in 1885-90, then Schönfliess in 1891 and then Barlow in 1894. See Sir Lawrence Bragg, the Crystalline State p.269. LH] (To Rose Bethe) Your father would know. [P. P. Ewald] I don't remember who discovered the 32 groups of symmetry around a point. That was much older, probably was in the mid-1800's. It could be Voigt, who was a very prominent crystallographer in the late 1800's.

Hoddeson:

Let me ask an institutional question. You published these two papers on solid state in the Annalen der Physik, whereas you published others in the Zeitschrift für Physik, those on helium, cathode rays and so on.

Bethe:

Yes.

Hoddeson:

Was there any difference in those days between the Zeitschrift and the Annalen?

Bethe:

Yes, the Annalen were willing to publish long papers, the Zeitschrift was not. And the Zeitschrift was more intent on having very new papers, new subjects. Now, it's true that the term splitting was also new, but it was very long, and so the Annalen was the natural place to publish it. The others were short papers. The Zeitschrift had the advantage that more people read it.

Hoddeson:

The Zeitschrift was the leading journal at that time, wasn't it?

Bethe:

Yes, what Physical Review Letters is today, in that most people read it.

Hoddeson:

There were longer articles in it occasionally. Sommerfeld's were longer, for example.

Bethe:

Yes. But then he was Sommerfeld.

Hoddeson:

Right. We never finished with the group theory work. You decided to learn it, and how did you do that?

Bethe:

Madelung did one thing for me in this respect. I told him I wanted to learn group theory, and he told me I should read the textbook by Speiser. [A. Speiser, Theorie der Gruppen (Berlin, 1923).]

Hoddeson:

That, I gather, was the main text.

Bethe:

That was the main text which was understandable by the theoretical physicists. It began at the beginning.

Hoddeson:

Who was Speiser?

Bethe:

I don't remember. He was a mathematician. I don't remember where he was.

Hoddeson:

But his text was very important.

Bethe:

Yes. It's one of the yellow books published by Springer.

Hoddeson:

I'll have to take a look at it. Now, you also mention a man named Ehlert in your paper. I don't know whether he had any significance for this history.

Bethe:

He was, I think, one of Sommerfeld's students. Is that possible?

Hoddeson:

Well, if it doesn't ring a bell, it's not worth spending time on.

Bethe:

It rings just a tiny bell.

Hoddeson:

I must have picked it up from the references in here. ["Termaufspaltung in Kristallen," Annalen der Physik 32 (1929), 133-208.] was trying to figure out where you learned group theory.

Bethe:

I learned it entirely from Speiser's book. And now, Ehlert? No, he had no special relation to me.

Hoddeson:

Now, just a couple of papers that appear to have a slight relevance to solid state. One is "The Passage of Electrons through the Electric Field in a Lattice". [Zeit. f. Physik 54 (1929), 703.]

Bethe:

Ah, this is not solid state. This again was one of Madelung's suggestions, so he did have some influence. Pohl had done an experiment in which he took a lot of wires which he charged alternately positive and negative, and then he let a beam of electrons go through that lattice. Some of the electrons would be deflected to the right and some to the left. In fact, he got two maxima, one on the right side and one on the left side. Well, Pohl wanted to show that you didn't need quantum theory, you didn’t need waves, to get these maxima, and wasn't it strange that you got two such maxima in a gross lattice — I think his wires were 2 or 3 millimeters apart — and this couldn't have anything to do with the de Broglie wave length. Indeed it didn't. And so, where was the significance of the Davisson-Germer experiment if you could after all make it in this different way? He was very surprised that you got two rather definite maxima. And so in my paper, I showed that indeed, with the Pohl arrangement, you should get two definite maxima, even though there was no wavelength, no diffraction. It is just the property of the electric fields in between these wires. Madelung's suggestion, as far as I know, was "Now look here, here is Pohl's paper. Clearly what he wants to prove is wrong. Davisson and Germer proved electron waves, so, try to show that Pohl's experiment can be explained and that it is not any argument against the Schrödinger equation." Which was a sensible suggestion on Madelung's part.

Hoddeson:

Was Pohl a major power at that time in the community?

Bethe:

Yes. Pohl represented the extreme experimental physicist who wanted to have nothing to do with theory, in contrast let's say to Gerlach who was very open to theoretical suggestions.

Hoddeson:

It's amazing that Pohl did so well with that attitude.

Bethe:

Right. And it's amazing that he had that attitude, or perhaps it's not so surprising, because Göttingen was a hotbed of theoretical physics, with Born and lots of other people. And of course, in Göttingen there was Franck, an experimenter who was extremely theoretically inclined.

Hoddeson:

There's another paper I don't have here, on the photoelectric effect, and I don't know whether that pertains to our discussion — "On Non- Stationary Treatment of the Photoelectric Effect," written in 1930. [Ann. d. Physik 4.4 (1930), 443.]

Bethe:

Ah, yes. That was one case in which I cooperated with Sommerfeld. Namely, Sommerfeld, after he had done his solid state theory, became mostly interested in the photoelectric effect made by x-rays; x-rays, let's say, of energies of 1 kilovolt to 10 or 50 kilovolts. So he was interested in calculating the cross-section of the photoelectric effect as a function of energy, and the angular distribution of the electrons which come out. And these are beautiful papers, but this is on the individual atoms. Now, he did all this by the time-independent Schrödinger equation, i.e., a stationary theory, so to speak. And he claimed that it would be very difficult to do this as a function of time. Stimulated by this challenge, I did it as a function of time, and showed that indeed the electrons come out. If you let the light come in beginning at time zero, then the electrons will come out, and at a given distance from the atom you will begin to see them first after a time distance divided by electron velocity. And that comes out very beautifully and very simply. It has nothing to do with solid state, but had a lot to do with Sommerfeld. And he was very pleased, because it involved integration in the complex plane, and anything which had integration in the complex plane was very pleasing to Sommerfeld.

Hoddeson:

Well, I think we're ready to talk about this big Sommerfeld-Bethe Handbuch article [A. Sommerfeld and H. Bethe, "Elektronentheorie der Metalle," Handbuch der Physik 24/2 (Berlin, Springer, 1933), 333-622.], certainly not everything in it but just a few highlights. Now, you mentioned how you came to write this, that Sommerfeld had been asked by the editor and agreed that he would do it if you write 90 percent of it. I was amused to count the number of pages —

Bethe:

Did I write 90 percent?

Hoddeson:

Well, he wrote 35 pages out of 289. And so if you approximate it as 30 to 300, it is indeed ten percent.

Bethe:

Right, very good.

Hoddeson:

The other night you said that it wasn't so difficult to write because there are not that many references.

Bethe:

Yes.

Hoddeson:

There are approximately 100, between 100 and 125.

Bethe:

That's not many for 300 pages.

Hoddeson:

That's right.

Bethe:

Nowadays you have that many in maybe 30 pages.

Hoddeson:

One thing that would be good to get on tape is the role that the Handbuch der Physik played in physics at that time. Was it something like the role today of the Reviews of Modern Physics? Or did it have another purpose?

Bethe:

It was supposed to be more permanent than the Reviews. And it wanted to cover the entire field of physics, from Volume 1 to 24. It was supposed to be an advanced textbook and not just a review of modern physics. So the early volumes are very classical physics. The later volumes, I believe from about 20 to 24, were modern physics. And so it have very similar content as the Reviews of Modern Physics, but it was just part of a bigger program.

Hoddeson:

I see. Now, essentially Sommerfeld summarized his two long papers of 1928. [Zeit. f. Physik 47 (1928), 1-32, 43-60.]

Bethe:

Right.

Hoddeson:

And you summarized everything else that had been done of significance in the following five years.

Bethe:

Yes.

Hoddeson:

Now, could Sommerfeld have done the quantum mechanics part himself or had he stopped working in the area?

Bethe:

No. He never tried to understand this.

Hoddeson:

I see. The next question was, did he work with you at all on your part? Did you discuss it with him?

Bethe:

Not very much. I showed him the manuscript, and I suppose he must have read a few pages of it. I think we discussed the general outline, but that was about all.

Hoddeson:

I see. Did you discuss it with anyone in particular?

Bethe:

No, I just wrote it, and there was essentially no editing. That is, the editor just decided it was not complete nonsense and they printed it pretty much in the way I had written it.

Hoddeson:

Did you have any particular problems in writing it that you remember?

Bethe:

No. Time.

Hoddeson:

Time was the main problem?

Bethe:

Yes.

Hoddeson:

You mentioned it took you something like six months, or was it perhaps even more?

Bethe:

It was about six months, maybe a little more. Of course I did other things in between, and I would think, six months is about the amount of solid work I applied to it. So it took about a year of which I spent half time on this.

Hoddeson:

So six months of full time.

Bethe:

Yes, of full time work.

Hoddeson:

Reading and writing.

Bethe:

Yes.

Hoddeson:

Did you at that time think you might become a specialist in the solid state area, or was solid state just a subject you were learning and explaining?

Bethe:

No, I didn't think so. In fact, I was just as interested in the one and two electron problems as I was in the solid state.

Hoddeson:

There are one or two themes that go through this article. One is the question, why does the free electron hypothesis work so well?

Bethe:

Yes.

Hoddeson:

And this is something that you eventually find some answers for in the paper itself.

Bethe:

Yes.

Hoddeson:

Now, the problems with the Sommerfeld theory that you mentioned, in the place where you begin writing, are: the temperature dependence of the conductivity, which is not explained; the magneto-resistance; and certain complicated thermoelectric effects which include the Hall effect.

Bethe:

Yes.

Hoddeson:

You use that reflection as a departure for going into things more precisely.

Bethe:

Yes, you're right.

Hoddeson:

And you derive the energy bands from the Kronig-Penney model [Proc. Roy. Soc. A130 (1931), 499]—

Bethe:

Yes.

Hoddeson:

—rather than going back to Bloch.

Bethe:

Bloch didn't go particularly into energy bands. Well, did he even have the idea of it? Did he emphasize that? The main emphasis in Bloch, I thought, was to show that you get free motion of electrons in a periodic potential, but I don't believe he emphasized that there are only bands which are allowed, at least that's not what I remember of his paper. The great thing in his paper is "no resistance in a periodic field."

Hoddeson:

That's certainly in there.

Bethe:

Yes. This was such an enormous discovery, that an electron going through a periodic field, no matter how strong, will move freely, completely contrary to any classical concept.

Hoddeson:

That had already been derived, wasn't it, by Rosenfeld and Whitmer?

Bethe:

I'm not aware of it. I think this is completely original with Bloch. Bloch wrote a very nice reminiscence about Heisenberg, which you may know in Physics Today, in which he describes how he discovered the free electron waves, and showed it to Heisenberg, not thinking much of it. And Heisenberg said, "Why, you have solved the problem." [F. Bloch, "Reminiscences of Heisenberg," Physics Today (December, 1976), p. 23.]

Hoddeson:

Right. I remember that.

Bethe:

So this really was the most important step in all of solid state theory, I think. Then, of course, I know that I went in great detail into the calculation of resistance proportional to temperature, and that was very interesting. And then of course this still left the question how do the electron wave functions actually look? And you tell me, I used the Kronig- Penney model, which was fine as a simple model, and that was all I had at the time. And when I had written a lot of the paper, then Wigner-Seitz came out.

Hoddeson:

Right. Wigner-Seitz came out quite late. The first Wigner-Seitz paper was published in 1933.

Bethe:

Right.

Hoddeson:

Both your paper and theirs appeared in 1933, so you must have quickly put in a section on the Wigner-Seitz paper at the end.

Bethe:

Right. I think that's what I did.

Hoddeson:

I'm very interested in the reception of the Wigner-Seitz work in Germany. Was it immediately recognized?

Bethe:

I know only that I considered it the answer to all my questions.

Hoddeson:

I see. And you got it from Physical Review you told me the other night, not from a preprint or anything like that.

Bethe:

There were no preprints in those days.

Hoddeson:

Well, they might have sent you a copy of their work earlier.

Bethe:

No. I don't think so. I think I just got it from the Physical Review.

Hoddeson:

So you immediately saw this as a turning point in solid state.

Bethe:

Yes.

Hoddeson:

I was wondering whether anybody else did at the time, but maybe not too many people were working in Germany by then?

Bethe:

I think that is correct. But I think you should ask Bloch and Peierls about their reaction. They were working on solid state theory, and it would be interesting to know. I think the three of us were really the main people working on solid state theory in Germany.

Hoddeson:

I may have a chance to ask Peierls in a few weeks. Let's go to the energy surfaces, pictured on page 400.

Bethe:

I remember I thought those were awfully pretty.

Hoddeson:

Yes. These are really Fermi surfaces. They're ideal Fermi surfaces, not real Fermi surfaces. Was this the first time they'd ever been sketched, to your knowledge?

Bethe:

I don't know.

Hoddeson:

As I mentioned to you the other night, there's some interest in figuring out when the concept began. You don't use the words "Fermi surface" here. You call them constant energy surfaces. Of course, they are Fermi surfaces.

Bethe:

Yes. It was clear that this would be important. And it surely was clear to me that they are, that they could be Fermi surfaces, but as you say I don't call them that. And it was also clear to me that it made a great difference whether they were nearly a sphere or were some interesting surface like this.

Hoddeson:

Here again I wonder if there was much interest in them at that time.

Bethe:

Yes, I think there was interest in that, but I don't believe people quite realized the significance. Well, I did realize the significance, in one respect. I had worked on the effect of a magnetic field on the resistance, and for that it was very important how anisotropic the Fermi surface is. And so, I think people were aware that this was important. And I was aware. I wanted it partly because of the Brillouin surfaces, and I think I describe those, don't I? Brillouin zones —

Hoddeson:

You've got something on it. Here on page 388, is a marvelously complicated Brillouin picture.

Bethe:

Yes. I had that wonderful man who indulged in making complicated drawings, so I didn't need to draw it, except very roughly.

Hoddeson:

They're very beautiful. Was there anything special about the man who drew these, Mr. R. Ruhle?

Bethe:

I never even saw him. I don't remember how we dug him up. I think he had drawn the figures for Jahne and Emde's tables of

Hoddeson:

I see.

Bethe:

And so we probably got him from Mr. Emde.

Hoddeson:

Did you pay him to do this?

Bethe:

Yes, sure, we paid him. I don't know how ml

Hoddeson:

(Flipping through the Sommerfeld-Bethe rE everything in here, so I am going to pick a few sect one on electrical contacts that I found very interes whether you drew upon some of this work later on, wh theory of rectification at the interface of a semico you were at MIT? [For reference, see below towards

Bethe:

I remember the work, yes. Yes, I remember ii in my mind, and until I had written the MIT paper, it always bothered me, what happens when two metals lie in contact. I am pretty sure that I was not the only person who drew these conclusions. I'm sure other people did too. Maybe Eckart had done this.

Hoddeson:

I think he had worked it out as an extension of the Sommerfeld theory [Zeitschrift für Physik 47 (1928), 38], but you went into much greater detail here, and it's much clearer. I was wondering, it looks as though this is a piece of original work.

Bethe:

Yes, well, Eckart had done some of it, and I think Eckart must have already seen that it is the Fermi energies which are the same. But I found it important to understand this.

Hoddeson:

Were you already thinking about the next step, semiconductors?

Bethe:

No. Not really.

Hoddeson:

In other words, rectification hadn't yet really become a concern for you.

Bethe:

No.

Hoddeson:

Although there, if you had been in touch with industries you might have picked up on that problem.

Bethe:

Yes, I would have. No, I was unaware of that.

Hoddeson:

Also later on in your work you give several references to Wilson's paper on semiconductors in 1931 and 1932, his classic work on semiconductors. But you don't go on to the work that he did a year or so later on rectification, where he did develop a theory involving a barrier. But in fact it was not quite right. He got the wrong direction of rectification. It wasn't until Mott and Schottky around '38 developed their theory that the direction came out right.

Bethe:

I was unaware of that.

Hoddeson:

You go on then to work on absorption and emission, and the photoelectric effect. We don't need to go through all of that. And you do a great deal with magnetism: paramagnetism; diamagnetism, where you use Landau, Teller and Peierls as your basic texts; and then ferromagnetism. Your piece on ferromagnetism suggests that ferromagnetism was of special interest to you.

Bethe:

Yes. Well, it was written at the same time as that meeting in Leipzig that I told you about.

Hoddeson:

I see, so you were really then studying that in great detail, and that's reflected in the way you treated ferromagnetism. Then you go on to do scattering of electrons. There you had a lot of personal expertise. And you go on to electrical conductivity and exchange with lattice vibrations.

Bethe:

Yes.

Hoddeson:

In that connection, the standard works were Bloch, Peierls, and Nordheim. I noticed another paper written by a man I hadn't come across at all, a Japanese names Fujioka. Does that ring a bell?

Bethe:

I have no recollection.

Hoddeson:

I notice he published in the Zeitschrift für Physik. He may have been a visitor in Germany.

Bethe:

He probably was a visitor in Leipzig.

Hoddeson:

Another Japanese worker who is mentioned is S. Kikuchi.

Bethe:

Oh, he was terribly important.

Hoddeson:

Oh, tell me about him. Is this the same man who then moved to Osaka and became the father of nuclear physics in Japan?

Bethe:

Yes. Correct.

Hoddeson:

I'm interested in his solid state work. He wrote a paper together with —

Bethe:

—with Nordheim. I'm pretty sure this is the same person. But anyway, the one who became the father of nuclear physics had done the most beautiful experiments on electron diffraction.

Hoddeson:

Oh yes, with Nishikawa, right.

Bethe:

I don't remember him.

Hoddeson:

The father of the present director of KEK.

Bethe:

I see.

Hoddeson:

Shoji Nishikawa who a famous crystallographer and x-ray diffraction person.

Bethe:

Yes. Well, Kikuchi, after the founders of the subject, Davisson and Germer and G. P. Thompson, Kikuchi was the next person who made a big contribution and found both dark and bright lines in the diffraction picture from a crystal in transmission. And I think this was explained but I don't remember the explanation. He was a brilliant experimenter. He came after the war to Cornell for a year or two. We invited him as a postdoctoral fellow, and he did some very nice work on nuclear photoelectric effects at energies like 200 MeV. So he's a very important person.

Hoddeson:

He must have been in Germany for a while, too.

Bethe:

I am sure that is correct, yes.

Hoddeson:

—in order to work with Nordheim.

Bethe:

Yes.

Hoddeson:

That's an interesting lead, because, of course, one is also interested in how these ideas are transplanted in other countries.

Bethe:

Yes. Now, I don't guarantee that this is the same Kikuchi. But pretty sure.

Hoddeson:

Certainly the man who did the Davisson and Germer type work is the same as the father of nuclear physics in Japan.

Bethe:

Yes. Right. That I know.

Hoddeson:

It probably is the same; it is the correct first initial. Superconductivity is worth saying a few words about, because that was the main unsolved problem, I gather.

Bethe:

That is correct.

Hoddeson:

And many people were working on it — Bloch, Landau, Kronig, Elsasser, Frenkel.

Bethe:

Yes. There was the Bloch theorem: "Every theory of superconductivity can be disproved." I don't know whether I mentioned that.

Hoddeson:

I don't think you mentioned it in here, or if you did, I missed it.

Bethe:

No, you would no

Hoddeson:

Let's see, on page 555 of the article, you comment first on Bloch's and Landau's work, which includes the idea of a finite electric current associated with the deepest energy levels. And then you go on to Kronig's idea of a linear chain of electrons moving without resistance through the lattice a theory you criticize but consider very promising.

Bethe:

It is really awfully good, what they say.

Hoddeson:

Bloch and Landau?

Bethe:

Bloch and Landau. Almost exactly right. It also says that one cannot consider single electrons. They really had an awful lot. The Kronig idea does not seem to be very close to the real superconductivity.

Hoddeson:

In a review article on the electron theory of metals, written at about the same time, in 1932, Peierls ends the review saying that the work on the subject seems to be done now: all the fundamental problems seem to be solved with the exception of superconductivity. [R. E. Peierls, Ergebnisse der Exakten Naturwissenschaften XI (Berlin, Springer, 1931), 264-322.]

Bethe:

Yes.

Hoddeson:

Was that really genuinely the feeling at that time?

Bethe:

Yes, that was generally accepted, yes.

Hoddeson:

You wrote a paper criticizing the Frenkel theory of superconductivity.

Bethe:

Yes.

Hoddeson:

Together with Fröhlich, in fact. [H. Bethe and H. Fröhlich, ZS. f. Physik 85 (1933), 389.] That's not mentioned here but that's in the bibliography. I haven't had a chance to look at these theories in detail yet.

Hoddeson:

I was curious about Pauli and Heisenberg. One would think that they would have been interested in a problem like this.

Bethe:

Not Pauli. No. Pauli, as we mentioned earlier, was not interested in anything that had to do with the solid state. [See however interviews with R. Peierls by L. Hoddeson in May and July 1981. LH.]

Hoddeson:

Even something that was such a big mystery?

Bethe:

Right.

Hoddeson:

There's a lot of material in here on the Hall effect, which you consider one of the "complicated effects". The other night I brought up the analogy which is made frequently nowadays between the Dirac hole in the infinite sea of electrons and the hole in semiconductors, and you reminded me that Dirac holes were not taken very seriously until after the positron was discovered. But that was in 1932. By the time you wrote this, the positron had been discovered.

Bethe:

Yes.

Hoddeson:

But you don't draw the analogy here, which suggests that there was still probably a lot of skepticism around. Or maybe it was just not such an obvious analogy at that time.

Bethe:

It's a different field. And in the solid, it was clear there was a finite number of states, so it was very obvious that an unoccupied state was a hole and how it would behave. In the Dirac theory, you had a continuum, an infinite number of states. It was hard to work with. It was very, very hard to make a finite theory of it. Whereas, it was clear that the hole in a conduction band was a perfectly feasible theory; if you wanted to you could calculate everything. So it was much simpler than the Dirac hole.

Hoddeson:

In introducing it, you make the analogy to many-electron atoms.

Bethe:

Yes.

Hoddeson:

Just as Dirac made that analogy in introducing his original concept.

Bethe:

Yes.

Hoddeson:

Everybody seems to have made that analogy in the beginning with the exception of Peierls who didn't go quite that far in his Hall effect paper, which really has the root of the concept in it. [R. E. Peierls, Zeit. f. Physik 53 (1929), 255-66, on p. 262.]

Bethe:

Yes. Well, that was the thing that people were familiar with, atomic spectra.

Hoddeson:

So it was natural.

Bethe:

Right.

Hoddeson:

Well, there are so many other subjects in here. (Flips through more pages). A subject that was not discussed in this article, and I was wondering if you might recall something about it, was defects, and also dislocations.

Bethe:

I didn't know anything about it at that time.

Hoddeson:

Yet they were beginning to become important in Germany just at about that time.

Bethe:

Yes. I'm trying to remember when I learned about defects. It was at Cornell, and I'm trying to remember whether it was before the war. I think it probably was. I learned about defects in connection with the theory of — yes, I learned about them during the war — namely, when I got interested in the yield stress of metals.

Hoddeson:

In connection with what work?

Bethe:

Penetration of projectiles through armor plate.

Hoddeson:

This was done at MIT?

Bethe:

No, this was done at Cornell before I had a clearance. And in this connection I learned that the yield stress increases when you try to deform the metal very very quickly, and so that must have been about 1940. I didn't know anything about yield stress or defects in 1933.

Hoddeson:

I see. It's an interesting historical question, why did it take so long for people to think of that concept? That's one that didn't require quantum mechanics really.

Bethe:

True enough. But you like to look at the ideal crystal.

Hoddeson:

I guess that was the point.

Bethe:

Yes.

Hoddeson:

It took a while to start looking at real materials.

Bethe:

It was clear at an early time that the shear of real crystals was much easier than the theoretical constants would indicate. Compression was very difficult, but it was very easy to shear a crystal, so the more technically inclined people certainly wondered about this. I read about it — I guess probably fairly late — in some discussion by Ewald, which also I think was part of the Handbuch about solid state. He points out that the yield stress is much lower than it ought to be; that's about as much as I knew.

Hoddeson:

It also started very late in the US.

Bethe:

Yes.

Hoddeson:

People didn't really start working on it in large groups until almost 1950, after Seitz wrote some review articles explaining it to people and calling it to people's attention.

Bethe:

Yes.

Hoddeson:

At breakfast a few days ago we began to talk about 1933. 1933 seems to have been a turning point in solid state physics for several reasons. One was the first Wigner-Seitz paper, which gave a realistic approximation method for dealing with real solids instead of just ideal ones.

Bethe:

Yes.

Hoddeson:

Another was the political situation, which caused people to move to other places and therefore change what they were doing.

Bethe:

Yes.

Hoddeson:

Now, you mentioned that if the Nazis hadn't come to power at that time, you might have done more in solid state.

Bethe:

Yes. Right.

Hoddeson:

Do you think that was quite generally true? I will also ask Peierls and Bloch.

Bethe:

Yes. Well, I didn't have much contact with other people while I was in Germany, and I think my case may have been different from others. But I imagine that probably, after a few more years, I would also have been captivated by nuclear physics. But it came earlier because I got into contact with people who were doing nuclear physics. England was full of nuclear physics when I came there in '33, and I think this had a lot to do with it.

Hoddeson:

Yes, '33 was a year when other people were going into solid state. People like Wigner and his students were beginning to work at that time.

Bethe:

Yes.

Hoddeson:

Slater was beginning to train people like Shockley and others, and Mott and Jones were building up a group.

Bethe:

Yes. In fact, Mott and I just interchanged roles at that time. He had been in collision theory, high energy collisions, relativistic effects in collisions, and now he turned to solid state. And I did the opposite. I don't know why he changed.

Hoddeson:

I don't know the answer to why '33 was a breaking point, but it certainly was.

Bethe:

Yes. It certainly was.

Hoddeson:

And that's when your long article came out also.

Bethe:

Yes.

Hoddeson:

which in a way summarized the whole field up until that point and served as a text for the next generation, which then went on in a somewhat different direction.

Bethe:

Mott is, of course, deeply in this historical investigation, and I'm sure he knows why he turned to solid state theory at that time.

Hoddeson:

Yes. I expect to find out soon. It's the beginning of modern solid state physics, in a way.

Bethe:

Yes. Right.

Hoddeson:

—with a new emphasis on real materials.

Bethe:

Yes.

Hoddeson:

By the way, one of my coworkers on the history of solid state project asked me to ask you what it felt like to be a refugee working in England. Was there a difference in the feeling in England and the feeling in the US a few years later?

Bethe:

Yes.

Hoddeson:

Could you say something about that?

Bethe:

I think it was simply this: that England had been used to having Englishmen and Commonwealth people in their universities and so we refugees were rather a foreign element, whereas America has been a country of immigrants from the word go, and so it was perfectly natural that there would be more immigrants. This time they were in somewhat different fields.

Hoddeson:

The final question has to do with the work that you did on rectification during the war, during the first two years of the war while you were at MIT.

Bethe:

Yes.

Hoddeson:

Now, was that something that you were assigned to do?

Bethe:

Yes.

Hoddeson:

Who assigned that to you?

Bethe:

Zacharias.

Hoddeson:

I see.

Bethe:

Zacharias was the, leader of a group, even a division, in the Radiation Lab, which had to do with rectification problems. He wanted to make use of me and asked me to join the discussions of his group, and said then at one point, "Well, there are these whiskers connected with the silicon crystal, which we have found are good rectifiers. How does it come about? Tell us then, write a little paper, a report, why that is so."

Hoddeson:

So at that point the Mott-Shottky theory had appeared.

Bethe:

Yes.

Hoddeson:

Actually I have not read this work that you wrote. It's an MIT Rad Lab report, but I have not been able to get a copy of it. [H. Bethe, "Theory of the Boundary Layer of Crystal Rectifiers." (November 23, 1942) Unpublished report 43-12 of MIT Rad Lab.]

Bethe:

Is that so?

Hoddeson:

I don't know where I can. There must be some, maybe at MIT.

Bethe:

Well, there must be at MIT. And I think all the Rad Lab reports are in some archive. But I don't know where.

Hoddeson:

You don't have one either?

Bethe:

I am not sure whether I have one. I may have one. And if I have one, I know where it must be. It must be in a certain filing cabinet in the basement of our lab. So I think the best thing you could do would be to write me a letter in August, asking me to look for that report. I think the chances are about 50% that I have one. [Subsequently located at Purdue University, "attic" of physics department. Copy at Urbana.]

Hoddeson:

It probably would be better for me to read it first before asking you questions on it.

Bethe:

Yes.

Hoddeson:

Then I can ask you more intelligent questions, if indeed it's not entirely self-explanatory.

Bethe:

It probably is pretty self-explanatory. It's a rather simple report, and I referred to that paper by Mott.

Hoddeson:

And then also the Schottky one.

Bethe:

Yes. What I remember is that I just took off on that paper and tried to simplify it and make some approximations which would make it more immediately applicable to the practical problem. I think that's what I did.

Hoddeson:

What about Los Alamos? Was there any direct impact of the work at Los Alamos on solid state physics?

Bethe:

No, not anything — wrong! We were very much interested in the equation of state at very high pressures, and you probably know that work. Most of it is contained in the paper by Teller, Feynman and Metropolis and maybe one more person, applying the Fermi-Thomas model to high density solids. That, was good work. I think that was perhaps the most important solid state work that was done at Los Alamos during the war. We wanted to know what happens when you compress metals to twice, five times, normal density. Other than that, I don't remember anything. No. I think that's about it.

Hoddeson:

Thank you very much. You've been extremely helpful.

Bethe:

You're most welcome.