Gregory Wannier

Gregory Wannier — the Princeton period (interview by K. Szymborski, June 18 1982) Pauli on the solid state physics: There is a famous remark… When I was at the Bell Telephone Labs he came to visit the Laboratory and was shown around by the highest officials, vice-presidents I think. He was going through for about a day and then he said 'Well, you have a very nice laboratory here. But it is really only just applied physics…' Princeton "there was a special arrangement between Princeton and Basel Universities. There was an exchange of two Ph.D.s for a stay of one year at the other university. It was awarded each year. All the faculties participated in this program, and I was the only physicist who happened to be sent to Princeton. I certainly would be considered extremely fortunate that I was able to get such a scholarship, because the education in Princeton was probably more important, well, at least as important as any previous education I had had. That was, now, specifically in solid state physics.

When I came to Princeton — of course I had to find a professor who would give me the advice — I went to Wigner. And I remember that Wigner had a large number of pre- and Post-doctoral students (Herring, Bardeen, Smoluchowski, Seitz, Boukaert) and all these people did beautiful work on the application of quantum mechanics to the solid. Particularly, group theory was first really carefully looked at. First, of course, group theory was applied to atomic spectra. But it was realized after a while that the group theory would have beautiful applications in solid state because of translational symmetry of crystals. And it was gradually worked out by these people — possibility of constructing the Bloch functions is really a group theoretical problem of the crystal considered as a regular lattice. This produced several excellent analyses of spectra classification, somewhat ahead of experiment because to get aspects of solids, apart from Hilsch and Pohl, they were pretty wishy-washy looking things. The crystals were not clean, and since they were not clean these spectra were all pretty broad and structure less. That had something to do with luck too. Just nobody had found, when I went to study (the problem) clear-cut spectrum for a solid body had never been seen. They were all broad, washed-up spectra and one thought that was going to the end of it. One was able to get these band spectra in molecules, but solid looked sort of hopeless.

But, anyway, that where my thing came in. I think, Wigner asked me do I want to work in solid state or in nuclear physics. Wigner was just shifting to the nuclear physics. I said I want to work in solid state. Then Wigner said to me: Well, there is one problem that has never been properly solved, that is how the insulating solids have an ultraviolet edge at which the absorption becomes very large. We don't quite understand wow it happens and how it can fit with the theory of Bloch I think; when I started it was considered more or less in contradiction to the theory of Bloch waves. In other words, one saw that when one viewed the crystal as a combination of atoms and assumed that the ultraviolet spectrum consists of transforming of transferring an electron from a chlorine ion to a sodium ion neutralizing both would be a very good explanation. But on the other hand there was an atomic picture which seemed to have been in contradiction with the notion that the Blanch waves the electronic states are all waves that go through the entire crystal. I was to 100 at and see what I could get out of it.

I remember the first term, which was the fall term. We essentially looked at diamond. I probably got the most perfect collection of absorption of ultraviolet and infrared by diamond and how different diamonds react differently. But it somehow all missed the point (?) and neither Wigner nor I could make heads or tails out of the properties of diamond. And then I remember Wigner saying 'Well, maybe we should look at theory. We are both much better at that.' In a sort of a way meaning that I had not got anything out of the experimental results. (Digression about the language of communication.) They spoke English with Wigner.

After the New Year I worked on the theory and learned of the idea of Frenkel excitons. It looked to me that there must be some bridge (that was also a local theory. The local theory here was that the electron goes from the ground state to an excited state to one atom. And that excited state travels through the lattice as a wave.) Then I looked at more carefully and the first thing I realized was that a lot of so called Bloch waves are constructed from atomic function by similar device (draws on the blackboard). Now, the point is that I had learned enough mathematics by that time to realize that this thing must be possible to invert this. For some reason nobody had thought of it. And the reason nobody had thought of it is that this functions were not normal. (Explains technical problem of notarizing the function on the blackboard) "It should have been seen by other people but it hadn't. And I think the point is that Bloch functions were just too new and the mathematical implications were not really thoroughly thought out."

It all came in about three months — January, February and March. Maybe April 1937. Out of these functions you can now construct a very refine form of an exciton, which is also often given my name. Which, namely, takes into account the effective mass that the electron would have in this band, and combines it with the localization ... due to… Therefore there is no contradiction between the idea that there are Bloch functions and the idea that there are localized excitations. (Problem of delayed acknowledgement) Experimental confirmation came from Gross in Leningrad. By the way, my papers had better reception in the Soviet Union than they had in the United States. Because, I think, I tend to use rigorous mathematics in my derivations, like this one. And on rigorous mathematics base physic conclusions. That is not an Anglo-Saxon way. Russian scientists have often the same approach. Therefore, it is not surprising that they were the first out with the confirmation of my conclusions. Then Slater was convinced of it and he proposed the name Wannier functions for it, for which I have to be very grateful (laughs), because without it I would not be nearly as well off.

Slater spent, accidentally, I think, a spring term as a guest-lecturer at the graduate college in Princeton and he associated very closely with the whole crowd of young solid-state physicists that were there because he was also a bachelor and therefore lived in the graduate college like we did and there was an easy camaraderie that I have probably rarely experienced since between all of us. I think it was extremely useful to Slater. He picked up all the implications of the Bloch function picture which essentially we, that group of us, Wigner's post-docs, worked out. I was the last one. Shockley is a one man that liked my type of work. I owe a lot to him because he opened up Bell Telephone Labs later to me. He liked this clean-cut reasoning rather than saying well, all the real fact of science come from experiment and we have to sort of adapt ourselves to the experimental evidence. Which is a way to do physics but is not my way.

Digression on Russian science "Suppose you imagine yourself a hundred years back, 1881 instead of 1981. Scientists could not travel, or it was very exceptional if they traveled. They heard of other scientists through publications and they might make contacts through letters and so forth. But, if you do it conscientiously you can do quite well without personal contacts. It is not the Anglo-Saxon way, but it is possible to work that way. That is essentially how the Russian scientists work. Like scientists everywhere had to work in 1880s.

(Anecdote about drinking in America) Life in Princeton: "We always had our meals together and there was lots of fun at the same time as discussions. The discussions were sometimes very lively. I remember taking some very high-brow mathematics classes from Herman Weyl. I never understood it and I would say until this day I do not know really what he was talking about. I do not remember seminars but I remember my discussions with Wigner which were quite frequent — about every two weeks. Moves to the University of Pittsburgh.