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Oral History Transcript — Dr. Eugene Wigner

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Interview with Dr. Eugene Wigner
By Lillian Hoddeson, Gordon Baym and Frederick Seitz
At the New Yorker Hotel
January 24, 1981

Listen to Wigner talk about the paper he wrote with Seitz on the interaction energy of metals.

Transcript

Hoddeson:

This is Lillian Hoddeson and I am at the New Yorker Hotel with professors Gordon Baym, Eugene Wigner and Frederick Seitz.

Wigner:

President Seitz.

Seitz:

Fred Seitz.

Hoddeson:

We're going to have a conversation about the period of Professor Wigner's life that he spent on solid-state physics. Could we begin with a bit of background? Your publications between 1923 and 1933 show you had an almost deal background for treating the kinds of solid state problems you took up between 1933 and 1938, which we'll be focusing on today. You have a background in chemistry, especially molecular structure. You did some work on the lattice structure of crystals in 1924. You worked on atomic physics including spectra, quantum mechanics, molecular spectra, elastic vibrations and group theory, especially in relation to atomic spectra. From this it appears as though a thorough treatment of the kinds of problems you later took up with Seitz, Bardeen and Herring was almost a natural consequence, especially since, as you mentioned to Tom Kuhn in your interview with him, [In 1963, copy available at Center for History of Physics] you seem to have been attracted to areas that were on the borderlines between disciplines.

Wigner:

In this case between chemistry and physics. Well, more physics than chemistry. Isn't that right?

Hoddeson:

I gather that your interest in solid state began before your work with Polanyi? You worked on molecules and group theory before that time.

Wigner:

No, you see, with Polanyi I worked together a good deal, but the most relevant part was my doctoral dissertation in which he was the so-called adviser. That was on the rate of chemical reactions, and that was very interesting and I think it was useful work. He was a wonderful person and I admired him very much.

Hoddeson:

But as I understand from one of your other interviews, you got interested in group theory.

Wigner:

Before that.

Hoddeson:

Before that?

Wigner:

Yes, I don't know if you know, it has a somewhat amusing history.

Hoddeson:

I would like to hear that history.

Wigner:

Well, I must go back. I was working as a chemical engineer in Hungary in a factory, when I received an invitation to return to Berlin as an assistant to the professor of theoretical physics, Richard Becker. At about the same time, I read the article of Born and Jordan on quantum mechanics, a basic article, and that made me confident that the job offered will be very interesting, and that I will be able to do some work which will enhance my interest and knowledge in physics also. However, when I got to Berlin, the job was not yet ready for me, so they gave me another job, to be an assistant to a crystallographer, Weissenberg.

Hoddeson:

Weissenberg?

Wigner:

Oh, you know that?

Hoddeson:

You mentioned it in your interview with Kuhn. He was at the Kaiser Wilhelm Institute?

Wigner:

Right. Then I shouldn't...

Hoddeson:

But you didn't tell the whole story there.

Wigner:

I see. The rest of the story is that he asked me, "How does it come that the atoms in crystals are so often located on symmetry axes or in symmetry planes? Why is that?" Well, I went home, thought about it a little while, and it was pretty obvious that if the atom is located on a symmetry axis, then two derivatives of the potential energy, both perpendicular to the symmetry axis, are zero, so that two of the three equations are already satisfied. On a symmetry plane, only one equation is satisfied, but even that is more than none.

So I went back to him and explained it to him. Well, Dr. Weissenberg was not very happy about that. He said, "We should have a more elegant explanation for that. Study a little bit crystal symmetry."

Well, I knew crystal symmetry a good deal, but I thought I'd read a book by — the name doesn't occur to me —

Hoddeson:

Let's see, Speiser?

Wigner:

No, no, that came much later. No. I will tell you. And I read it, and then I had a more elegant proof for this. But what was more important, I learned a good deal of group theory, and that helped me very much in later life, so that sometimes somewhat less than absolutely reasonable suggestions have favorable effects. I'm sorry that I don't remember the name.

Seitz:

You don't mean Schoenflies?

Wigner:

No, Schoenflies...

Seitz:

...is much earlier.

Wigner:

...is much earlier, and this was a book on general mathematical physics in which one section was on group theory, and the different sections were written by different people. I can find the book probably and give you the name, but it's really not so important.

Hoddeson:

Then did you try again to please Weissenberg?

Wigner:

Oh yes, and I pleased him this time, but this work was never published. But that doesn't matter. I got a job anyway as an assistant of Richard Becker, and soon enough an article of Heisenberg came out.

Hoddeson:

This was in Gottingen?

Wigner:

Heisenberg was in Gottingen.

Hoddeson:

And Becker?

Wigner:

No, Becker was at the Institute of Technology in Berlin, and he was an excellent teacher and wrote some very, very good books on theoretical physics. But this is how I learned group theory.

Seitz:

He went to Gottingen later.

Wigner:

He went to Gottingen later.

Hoddeson:

Then the next time you came back to this was after Heisenberg's paper on the many-body problem appeared in 1926?

Wigner:

Right. And of course I realized pretty soon which parts of it were in error.

Hoddeson:

Heisenberg's paper?

Wigner:

Yes, but the basic idea was just the same fascinating, and I extended the work to a three-particle case, and that I did myself. Then I showed my result to a friend who was a marvelous mathematician, a very close friend.

Hoddeson:

Oh, I know, John von Neumann.

Wigner:

Right. Right. Right. And he thought a little. As usual, he went to the corner of the room, mumbled, looking up, and then came back and told me, "I get you a copy of an article of —" You know, names don't come to my mind, but this should come.

Hoddeson:

What was the article about?

Wigner:

About representation theory.

Seitz:

Schur?

Wigner:

I. Schur — yes, right, Schur, well, you see, he remembers it better, but there was some collaborator, Frobenius. I can tell you where the article was published. It was published by the Prussian Academy of Sciences.

Hoddeson:

In that circle of people you were working with in Berlin, was there much interest in group theory at this time?

Wigner:

No. On the opposite. Schroedinger coined the expression, "Gruppenpest" must be abolished.

Hoddeson:

I see. I didn't realize Schroedinger...

Wigner:

Of course, you know his name.

Hoddeson:

I know his name but I didn't realize he was — I've certainly heard about the Gruppenpest.

Wigner:

You heard about the Gruppenpest.

Hoddeson:

Did you interact with Hermann Weyl?

Wigner:

No. Never.

Hoddeson:

I noticed in his paper on quantum mechanics and group theory that he refers to your work on that in a somewhat strange way.

Wigner:

Yes.

Hoddeson:

Almost as though he's dismissing it. [See H. Weyl, Zeit fur Physik 46 p. 1 (footnote).]

Wigner:

Yes. I don't know why that is. I read it and I didn't agree with him in that.

Seitz:

He could be difficult at times although he became more friendly and relaxed later in life. I know his son Joachim very well — a wonderful person. Did you know him Eugene?

Wigner:

Very vaguely. I knew Herman Weyl quite well but I never was close to him; I don't know why. Here it is, one of Schur's articles is quoted here, and it is quoted in the BERLINER BERICHTE, which is the Berlin Academy's paper.

Hoddeson:

Well, let's see. Later in Gottingen you then applied some of these ideas to describe properties of molecular spectra with Witmer?

Wigner:

Right. Right.

Hoddeson:

Also then later to the relativistic theory of electrons.

Wigner:

Yes.

Hoddeson:

And the quantization of the exclusion principle, so you certainly had a lot of experience.

Wigner:

Yes, it is a very useful subject, group theory, in many ways.

Hoddeson:

Before we move to the work that you did with Seitz, I just want to ask one quick question about the paper on para- and ortho-hydrogen, which has some relevance to solid-state theory.

Wigner:

Say, you know my articles better than I do. Yes. This also is based on group theory, to a large extent.

Hoddeson:

That's the famous paper, which had, I gather, great relevance for statistical mechanics.

Wigner:

Oh, I don't know. My estimate is not correct. I estimated in that article that the transformation time is 20,000 years. In reality it is 100,000 years. But it's longer than we usually wait for a material to transform by itself.

Hoddeson:

How did you happen to choose to do this problem? Did it come out of your chemistry background?

Wigner:

Well partly out of my chemistry background, but of course, I was closely relating to Polanyi who still worked at the Kaiser Wilhelm Institut Fur Physikalische Chemie, and I see that it is dated from there.

Seitz:

There was also a lot of excitement. It even appeared in the San Francisco newspapers.

Wigner:

I did not know that.

Seitz:

It attracted international attention in the popular press.

Baym:

What year was this?

Wigner:

Well, this was about 1933.

Seitz:

It would have been approximately '29.

Wigner:

You think it was '29?

Seitz:

I'm talking experiments, not your work.

Wigner:

Yes, well, I look for the experiments — you are right, Bonhofer and Harteck made the discovery. They found the two types of hydrogen.

Hoddeson:

Let's see, now this is a question that I would like to address to both of you. When you came to Princeton, you were not yet working on solid state.

Wigner:

No.

Hoddeson:

Until Seitz came to be your student.

Wigner:

Yes.

Hoddeson:

I gather you (Fred Seitz) were working with Condon first?

Seitz:

I started out as his assistant, yes.

Hoddeson:

You started out doing a problem on double refraction, wasn't it?

Seitz:

That's right. I don't think it was very good.

Hoddeson:

Then you started working on the group theory, and the question I had, in looking at your material, was: did you start the group theory work before you became Wigner's student?

Seitz:

Yes.

Hoddeson:

And if so how did you happen to pick that?

Seitz:

I got interested in crystals.

Hoddeson:

Was there anybody there who particularly...

Wigner:

Condon was not.

Seitz:

Condon gave a course on the optics of crystals. It was copied straight out of one of Frenkel's books. And I got interested in it, as one can do. And started working.

Hoddeson:

I see.

Seitz:

In the meantime your (Wigner's) book had appeared on group theory. [Eugene Wigner, Gruppentheorie und ihre Anwendung auf die Quartenmechanik der Atomspektiren; (Braunschweig: Friedr. Vieweg, 1931; reprint Ann Arbor: Edwards Bros., Inc., 1944).]

Wigner:

When was that?

Hoddeson:

I think '31.

Seitz:

The end of '31.

Wigner:

I see.

Seitz:

I remember it was in the Princeton Bookstore when I arrived.

Wigner:

But it was in German.

Seitz:

Yes. Well, remember, in those days, we all had to read French and German...

Wigner:

Yes. Now we have to read Russian. But some of the German papers are very interesting also.

Seitz:

It was an interesting time. But his work was well rounded. I mean, it encompassed all these things.

Wigner:

...crystal structure...

Hoddeson:

(To Seitz) So you were working on group theory, representations and you came across the book in the bookstore. And then what happened, did you go and speak with Professor Wigner?

Seitz:

Well, it was after he had left. We only crossed paths for a few hours. He gave his final lecture in January and then went back to Europe, because he was on half time.

Wigner:

That is right, but I thought...

Seitz:

And you came back again next fall.

Wigner:

Next fall, right. But then we met.

Seitz:

Yes. In the meantime, I'd got into these other things.

Wigner:

Which other things did you get into?

Seitz:

The crystal groups and so forth.

Wigner:

I see.

Hoddeson:

You were particularly interested in the irreducible representations...

Seitz:

Of space groups.

Wigner:

Yes, and he was the first one who determined the irreducible representation of all space groups, and that is a very significant work that he carried out.

Seitz:

The important thing was that Condon was completely tied up with his book with Shortley [Condon, E.U. and Shortley, O.H., The Theory of Atomic Spectra, reprint (Cambridge University Press, 1935).] and so I started working with Eugene (Wigner).

Hoddeson:

I see. Now, when you started working with Eugene — if I may call you Eugene — did you start on the subject of the groups, to continue that, or did you then switch to this new subject of sodium?

Seitz:

The new one.

Hoddeson:

How did that switch come about?

Seitz:

Well, he proposed that it might be a good problem if we could find a way to do it.

Hoddeson:

I see. Had you been thinking about that for some time?

Wigner:

Well, yes, a good deal. Because there were some articles of Sommerfeld, Heisenberg, also Bethe, isn't that right?

Seitz:

Yes.

Wigner:

I see. But certainly Sommerfeld and Heisenberg and Felix Bloch contributed to it very much. But they all contributed, only in a more abstract way. They were not interested in the structure of the crystal. They were interested in the electrical conductivity, and they used an approximation there, which was very similar to the approximation, which Witmer and I and also many other people used on molecules. But they did not fully admit that all these are rather good approximations. They treated the electrons in the crystal as free particles. Fred, please correct me if I am misstating things. And I realized that there is much more deeper thinking possible about it, which explains why the crystal exists. What is its binding energy? And that these theories of conductivity are approximations. And I thought it would be good to say something on the binding energies of the sodium atoms or the metallic atoms in general. I don't know who suggested that we treat sodium. I think it was partly because we knew that the valence electron in sodium can be treated as if it were in a potential, and the potential was determined. [Wigner, E. and Seitz, F., "On the Constitution of Metallic Sodium," Phys. Rev., 43 (1933) pp. 804-810; Wigner, E. and Seitz, F. "On the Constitution of Metallic Sodium," Phys. Rev., 46 (1934) pp. 504-524 Prokofjew, W. Zeits. fur Physik, 58 (1929) p. 255] I think that was you —

Seitz:

We found this paper of Prokofjew which had a field —

Wigner:

— you see, he remembers it better. Prokofjew, yes. And I think you found that. I don't know. It's irrelevant really.

Seitz:

It is in the literature.

Wigner:

Yes. And then we realized soon that if we assumed that the conduction electrons are in a potential, the Hartree-Fock approximation is relatively easily obtained. Now, I don't know whether you want us to explain what is the Hartree-Fock approximation.

Hoddeson:

No, it's not necessary to explain the physics, but to concentrate on the connections. Unless there is some point of the physics that is relevant to the story in a way that we might not know then it probably is useful to put it in.

Wigner:

Then let's say, the Hartree-Fock approximation is the approximation that these electrons move independently of each other, and that these electrons move independently of each other, and that there is no correlation between their positions. And I think it was you who calculated it — from group theory we learned that it is not difficult to calculate the normal states. It is only to be noted that, on a certain surface which is now called Seitz-Wigner cell's surface (which is a foolish thing) that the derivative perpendicular to the surface is zero. And Fred solved the problem with these boundary conditions in the potential. I think you remember that?

Seitz:

Yes. We found a way of doing it.

Wigner:

You found a way. But we don't have to argue this for a spherical surface which is a good approximation to this Seitz-Wigner cell surface, you calculated it. And, as a matter of fact, I produced the proof that this is a very good approximation.

Seitz:

For sodium.

Wigner:

For sodium, yes. But then the result for the binding energy or heat of vaporization that one obtains in this way was very, very low. Instead of the experimental, which is I think 27 calories, it was about six calories, so that we were attracted to the point that we have to improve the calculation and this brought us to the introduction of the so-called correlation energy.

Baym:

At this point, who did the calculation of the exchange energy of the free electron gas?

Wigner:

The free electron gas exchange energy — and you are right, that is very important — that was included in these six calories. That, I think, was...

Seitz:

Oh, you did that on the way back, on the boat.

Wigner:

On the way back to Europe?

Seitz:

When you went back to Europe once more.

Wigner:

Yes. Very true. And I did it on the boat. But I think it was done simultaneously by F. Bloch. Or not?

Seitz:

Quite possible.

Wigner:

I believe so. But it was independently done and published by us also about the same time. But even when that was included, the calculated binding energy was very small. So that we started to improve the calculation, and this led us to the words "correlation energy" which we estimated — there is no accurate calculation known for it even now.

Hoddeson:

Now you're talking about the second paper on sodium.

Wigner:

Yes.

Hoddeson:

In which you do a Hartree-Fock?

Wigner:

No, the Hartree-Fock theory is what is improved on.

Seitz:

There is a separate paper by Eugene, on the correlation energy law. [Wigner, E., "On the Interaction of Electrons in Metals," Physical Review 46, (1934) pp. 1002-1011.]

Wigner:

Did I do a separate paper on it?

Seitz:

mp3On the correlation energy. You did that in Budapest that summer.



Wigner:

See, he has a marvelous memory.

Hoddeson:

Are you talking about Wigner's paper on the interaction energy of metals?

Wigner:

— of electrons in metals. Now, you see something here that should bother you, in this article, namely that the names are given, "Wigner and Seitz," rather than "Seitz and Wigner". And I have been —

Seitz:

Oh, I handled that publication because you were in Europe.

Wigner:

Well, you know, the fact is that soon after this time, in '34 or so, I was told to look for another job. And I felt, therefore, that it is critical for me to appear as somebody who has contributed to physics. Fred, as soon as he was through with his doctoral dissertation, had four offers of a job. I had none. So I thought it is good if I put myself forward. But I don't think you should publish this fact. You should not publish it. You should blame me for something, perhaps, but —

Hoddeson:

Now, let me see. In the second —

Wigner:

— but I did get a job, eventually, yes, at the University of Wisconsin.

Hoddeson:

In the first of the two Wigner-Seitz papers on metallic sodium, you used that very physical approximation of the Wigner-Seitz cell and boundary condition, and you solved the equation there; it's one electron.

Wigner:

Yes, we did.

Hoddeson:

The problem. In the second one, you attempt to do the correlation —

Wigner:

— let me see whether it was —

Seitz:

— you have the correlation results in this paper you published later, as I remember, they were incorporated.

Wigner:

(reads) "The question of correlations between electrons with parallel spin is investigated quantitatively and the Fermi" — yes, you are right. We have it already included here.

Hoddeson:

At some point in that paper, though, you say that a more complete treatment of this will follow by one of us, and that's the third paper, the one by Wigner alone. You don't actually do the perturbation calculations in the second paper.

Seitz:

It's in the third.

Hoddeson:

It's in the third, and in the second paper, you sort of guess a solution, is that it?

Seitz:

It's based on the other, I think it's — you know, it's a long while ago, but I think it's an empirical fit.

Baym:

Interpolation.

Seitz:

Interpolation. But Eugene had done this in Europe, in the summer of '33, but we had the results, and we incorporated them in the second paper.

Wigner:

You remember things much better, than I do.

Seitz:

Well, you were already working on nuclear physics by that time, so this is a small part of your research at the time.

Wigner:

I remained interested in solid-state physics for a long time, even though I didn't write many articles on it. And I read all your articles, as you probably know. You know that Dr. Seitz wrote a book on solid state physics, which is — well, even now one of the best and most informative books.

Hoddeson:

A lot of the later work that was done on band theory was based on the first Wigner-Seitz paper.

Wigner:

But some of it was entirely group theoretical, and three people together, Bouckaert, Smoluchowski, and myself [Wigner, E. and Seitz, F., "On the Constitution of Metallic Sodium. II," Phys. Rev., 46 (1934), p. 509. Bouckaert, L.P., Smoluchowski, R. and Wigner, E., "Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals," 50 (1936), pp. 58-67.] — by that time I had a job so we put the authors' names in alphabetical order — it was entirely group theoretical and explained how, at the top and at the bottom of the zone, the derivative of the energy with respect to momentum is zero, that several wave functions have the same energy, and so on. That was entirely group theoretical.

Hoddeson:

That was done much later, in 1936.

Wigner:

Yes, that was after I returned to Princeton?

Seitz:

No, right at the end of your Princeton period.

Wigner:

That was at the end of my Princeton period, when I was, so to say, told to look for another job. Wisconsin, yes.

Seitz:

I think you went to Wisconsin in '36.

Wigner:

I think you're right. That's the way I remember it too.

Hoddeson:

Before we go to that paper, which I would like to discuss also, I'm still having some trouble with this series of three papers. I'm trying to understand in what sense these were seminal papers. It appears to me, the first paper was one that was used by everybody.

Wigner:

What does it mean, "used by everybody"?

Hoddeson:

Well, Slater and his group, for example, took that as a starting point and then — improved.

Wigner:

— Oh. I see — by seminal paper, you mean a paper which led to other papers.

Hoddeson:

In fact this one led to a whole industry, I would say.

Seitz:

But they were not interested in the quantitative side very much but more on the qualitative structure of the bands. How did they look in diamond, how did they look in this, and so forth. Whereas we tried to work on the binding energy; that was the goal. What are the sources of binding in a quantitative sense? And there weren't many people interested in that. John was.

Wigner:

John Bardeen.

Seitz:

And of course, Conyers Herring. The later school was not.

Wigner:

I thought Slater also wrote a paper on the binding energy and reproduced pretty nearly our paper with very few improvements.

Seitz:

— I don't remember that.

Hoddeson:

Well, there is a reference to a Slater paper, in here somewhere — a 1934 paper. You say, "In a recent paper which has appeared while this manuscript was in preparation," (this is the second paper now) "Slater has investigated this phase of the problem", [Wigner, E. and Seitz, F., "On the Constitution of Metallic Sodium. II." Phys. Rev., 46 (1934) p.515.] and let's see, the side of the problem that you're discussing now is the Fermi energy. There's a reference to it, but I haven't had a chance to look at that paper yet. He says, "He made a formal solution satisfying the proper boundary conditions at the centers of the eight hexagonal faces of the S-polyhedron which required a general function of and so on.

Wigner:

The S stands for Seitz.

Seitz:

No, it was "spherical".

Wigner:

No, a polyhedron cannot be spherical.

Seitz:

But we approximated it by a sphere.

Wigner:

Yes, but the S-polyhedron is — well, we don't need to argue.

Seitz:

Slater had one paper in which there was a wrong calculation of the exchange. I think he got a factor of 2 too large.

Wigner:

Oh, no. Really?

Seitz:

And so that he didn't seem to need the correlation energy. He had the electrons of opposite spin being correlated through the exchange, which couldn't be.

Wigner:

Yes, you are, right.

Seitz:

We never pointed that out.

Wigner:

No, no, it's not polite.

Hoddeson:

Was there much interaction between your group at Princeton and Slater's group at MIT in that period?

Wigner:

No. No, virtually none.

Seitz:

I knew the younger people very well. Shockley was part of it, and there was [Harry] Krutter and a couple of other people. We'd meet at meetings and compare results.

Wigner:

Oh, I didn't know that.

Hoddeson:

I understand that there were exchanges a little bit later. When I interviewed Jim Fisk he recalled that there would be meetings; people from one of the schools would travel to the other, and exchange views. Do you remember that? That may have been later.

Seitz:

No, I think mainly at the Physical Society meetings, which were a lot smaller than they are now.

Hoddeson:

That met in New York at that time, isn't that true?

Seitz:

Washington also, at the Bureau of Standards at the time of the big spring meeting. The January meeting was here in New York originally at Columbia and then in this hotel.

Hoddeson:

Really?

Seitz:

When it outgrew Columbia.

Hoddeson:

I see. So there was not really much exchange, except...

Seitz:

There were colloquia. You know, you would be invited to give a colloquium talk.

Hoddeson:

I see. But you wouldn't send the equivalent of preprints to each other, or would you?

Seitz:

It wasn't as common then. It might happen, but now, it's almost an independent channel of publication.

Seitz:

It wasn't then. THE PHYSICAL REVIEW came out, I think, monthly, and was about that thick (1/3 inch).

Wigner:

You had to see when it was received and when it was published —

Seitz:

Publication took six months or so. Well, they sent it out to review.

Hoddeson:

Here, we can tell. This paper on the interaction of electrons in metals was sent in October and published December.

Wigner:

You see, that is a relatively short.

Seitz:

— that was unusually fast —

Hoddeson:

Now, in this paper Wigner that for his kind help in connection with the preparation of this manuscript. What role did you in fact play?

Seitz:

I guess I read it.

Wigner:

Oh, this is on the correlation energy —

Seitz:

I think you actually sent that to me from Europe, and I went over it and we had it typed in the office.

Wigner:

Gee, I find it difficult to remember.

Hoddeson:

Is this where the term "correlation energy" dates from, from these two papers?

Seitz:

Yes, here's where it got identified as an entity.

Hoddeson:

Right. In this third paper, the Hartree-Fock problem is set up. The high density limit is treated in a perturbation theory way. The Rayleigh-Schroedinger perturbation theory, it's called in this paper.

Wigner:

Yes.

Hoddeson:

And then Eugene makes what I think is a new contribution in connection with the low density case, pointing out that they form a lattice.

Wigner:

— that's the high-density case. No?

Seitz:

Also at the low density. It's a different kind.

Wigner:

You are right.

Baym:

Nowadays we all speak of the Wigner lattice. This is the paper where it is introduced?

Seitz:

That's right. That's right.

Hoddeson:

It's just introduced at the very end, almost as a comment. Most of the paper has to do with the Hartree-Fock approximation.

Seitz:

That's the basis for the calculation. Which is justified by the fact that at the normal density, it's almost valid.

Hoddeson:

Now, did this paper attract a lot of attention at that time?

Seitz:

Not particularly.

Wigner:

The joint paper did.

Seitz:

Yes. That started a lot of things going. It was probably Herring who picked these things up and dealt with them.

Wigner:

Herring was wonderful, and he has not been recognized.

Seitz:

Well, the Academy gave him a well-deserved medal for his work last year.

Wigner:

Oh, good. Oh, good. I am so glad to hear that, because I really admire him very much, and of course he was not so interested in success; he was interested in knowledge, and he knew the literature and the subject better than most anybody, I would say.

Seitz:

He has the best memory.

Hoddeson:

Now, I have one or two questions about this third paper before going on. The correlation energy. You say it did not attract much attention, except from a few people like Herring who were interested in it but didn't —

Wigner:

— Well, Fred was interested in it.

Hoddeson:

Did you use it in any of your work? At that time?

Seitz:

Well, I made a big thing of it in my book. A student at Rochester and I tried to go to a higher approximation but never got anywhere.

Wigner:

Oh. I didn't know that.

Seitz:

Well, it never led to anything.

Hoddeson:

Now, years later, in the 50's, the high density case was treated better, using field theoretical methods.

Wigner:

Yes. And that showed that this approximation is not valid in that case, because they had a logarithmic term, which I did not have. But of course, sodium is very far from the high-density case.

Baym:

Your calculation here is of order E4.

Wigner:

Yes, it was.

Baym:

Take an E4 log.

Wigner:

Right. You seem to know a great deal about solid state physics.

Seitz:

That's his business.

Hoddeson:

He is now in astrophysics, but he sometimes looks over my shoulder when I'm preparing for an interview.

Wigner:

I see. I thought you were in astrophysics.

Hoddeson:

Now, Bohm and Pines got interested in that general area around 1951 and I was wondering whether Bohm got interested in it partly because he was at Princeton and you were also at Princeton. This is of course much later now. We're skipping to a later period.

Wigner:

We had very little contact, Bohm and I, and in many things I disagreed with him. He was in favor of the so-called hidden variable theory. He still is, I believe, in favor of it. Although I just have an article by him, which I brought to read, which treats an entirely different subject, on the validity of superposition measurements. So, we did not have close contact. I disagree with him on many subjects, in fact on most.

Seitz:

After the war, a whole new group of people began to get a broader interest in the many-body problem, and developed new techniques to try to handle it.

Hoddeson:

I gather it was partly because there were so many more people being trained at that time in the new methods that were being developed in the late forties.

Seitz:

And also superconductivity was the big challenge, and unexplained. It drew a lot of attention.

Wigner:

May I ask you, do you fully accept the Bardeen-Cooper-Schrieffer superconductivity theory?

Seitz:

That's a hard thing. I think it is by far the best theory we have of the phenomenon.

Wigner:

Superconductivity theory, yes. But that also tells me that you agree with me that it isn't a full explanation. It's funny, "the best" means that it isn't good, it isn't complete.

Seitz:

It's a tremendous advance.

Wigner:

Yes, indeed.

Hoddeson:

Let's see, the next paper in this series of solid state papers that I wanted to discuss briefly with you is the paper on the theory of the work function which you wrote with Bardeen. This is one of the early attempts to calculate an important physical quantity which was measurable.

Wigner:

Yes, and has been measured.

Hoddeson:

I was wondering, did you suggest this paper? [Wigner, E. and Bardeen, J., "Theory of the Work Functions of Monovalent Metals," Phys. Rev., 48 (1933), pp. 84-88.]

Wigner:

Yes, I suggested it.

Hoddeson:

How did that come about?

Wigner:

Well, it was obvious to me that it is an important question, the work function, because you know, the radius and what do you call those ...

Seitz:

Vacuum tubes.

Wigner:

Vacuum tubes are based on it. And I suggested it, that we work on it. And he was very helpful. I don't think they are very wonderful papers, but they at least called attention to the necessity to consider the question, and we came to quite reasonable results.

Seitz:

It was a very courageous thing, because you're dealing with the surface.

Wigner:

Yes. The surface is very different from the inside. But it was not so important.

Hoddeson:

Why do you say they're not very wonderful papers? They've been very widely referred to.

Wigner:

Is that so? I didn't know that. (Laughs)

Hoddeson:

Well, perhaps because so many measurements have been made of the work function, and it was perhaps the only thing people had. I was wondering what you didn't like about the papers.

Wigner:

Well, the way Mark Twain put it, "I could have done it with one hand tied behind me". But Bardeen was and is an excellent physicist and you know that he has contributed to physics very significantly.

Hoddeson:

I think this work on the work function was something that preoccupied him for many years, and in some ways it connects directly with his contribution to the transistor.

Wigner:

That is so. But you see, he had one wonderful quality, that he didn't change the subject of his interest too often, and therefore he could make very important contributions. Well, you know him probably very well. What is he doing now?

Baym:

It will come to me in a moment, go on.

Seitz:

He gained an understanding of the surface which practically no one else had, as a result of this and what followed. So when the initial Shockley field effect experiment failed, because of surface states, it was Bardeen who recognized what was happening.

Hoddeson:

Right. And then later, a year and a half or so afterwards, the series of experiments that led to the transistor had to do with studying the work function, which Brattain at that time was doing. He noticed some funny things when the temperature was changed that had to do with condensation of water, I think, and that got Bardeen immediately involved because he was very much involved with surfaces, and from then on the two of them did a series of experiments.

Wigner:

This did not impress me as much as the Bardeen, Cooper and Schrieffer paper.

Hoddeson:

Well, the superconductivity theory was a much more fundamental breakthrough in physics than the transistor.

Wigner:

Yes. Bardeen, I have very high regard for him also. Altogether I admired my first three students enormously.

Baym:

He's now doing electrical transport from charged density waves. From tunneling charged density waves.

Wigner:

What kind of charged density waves? What is a charged density wave?

Baym:

When the electron distribution is essentially not uniform to first approximation, but rather has a periodicity which is not commensurate with the lattice periodicity.

Wigner:

Thank you. That's very interesting. But you see, he sticks to the subject. He is in solid-state physics. And it matters.

Seitz:

The same is true of Herring.

Wigner:

Yes. But Herring is more devoted to the literature.

Hoddeson:

I gather you didn't work quite as closely with Herring as you did with Seitz and Bardeen?

Wigner:

No, I like Herring very much, and we worked together vigorously. We did not always agree on every question, but I had a very high regard for him.

Hoddeson:

I wasn't questioning that. Let's move on to the Bouckaert-Smoluchowski-Wigner paper.

Wigner:

Good.

Hoddeson:

Which I gather was especially important in semi-conductor work, because it told people how they can restrict themselves. How did that paper come about? I'm particularly interested in this collaboration between the three of you on the group theory paper. Do you remember?

Wigner:

Well, Smoluchowski is in Princeton.

Seitz:

No, he's now in Texas.

Wigner:

Yes, right now he's in Texas, but he's still fundamentally in Princeton. And, well, I thought it's an amusing thing to look at it from a group theoretical point of view, what follows from the association of independent electrons, i.e. disregard of the correlations. This approximation has proved, in many ways, useful and more accurate than I ever suspected. You know, I was devoted, so to say, to the correlation energy, because I felt that is very important, and that is, of course, what I am missing in the Bardeen-Cooper-Schrieffer theory. But I thought, well, let's look at the problem from group theoretical considerations for the independent particle model, and that is why we worked on it, and it wasn't difficult. The Bouchaert, Smoluchowski, Wigner is also a paper which either of us could have written with one hand tied behind him. Isn't that true?

Seitz:

Well, I wouldn't go that far.

Wigner:

Perhaps only one hand holding up a heavy weight.

Hoddeson:

What was the nature of the collaboration? Did the three of you discuss it together and —

Wigner:

— yes, they came to my office and we discussed it and we decided that we look at all crystal classes, and such things, and —

Hoddeson:

I gather it was your idea to start with?

Wigner:

Yes. The subject, I think, was suggested by me but that did not solve it.

Hoddeson:

No. And Bouckaert and Smoluchowski were sort of fellows at that time?

Wigner:

Yes. Bouckaert of course is in Belgium, but he was for a year in Princeton. And Smoluchowski eventually remained in Princeton; and he maintained a great deal of interest in solid-state physics. Isn't that right?

Seitz:

That's right, yes. I don't know what's become of Bouckaert. I have not heard from him since the war.

Wigner:

I saw him when I was in Belgium, and he seemed to be quite happy. And I have high regard for him also.

Seitz:

Is he in Brussels?

Wigner:

I think he's in Brussels, but that is one thing that I don't remember.

Hoddeson:

This paper I gather also led to a whole group of other papers, in which this basic approach was extended.

Seitz:

Yes.

Hoddeson:

So it's also a seminal paper in that sense.

Seitz:

That's right.

Seitz:

Well, it's tied in with the reduction of space groups.

Wigner:

Yes, you're right. But of course the representation of the space groups were all determined by Dr. Seitz.

Hoddeson:

We'll have a chance to speak about that on Monday, I hope.

Seitz:

Monday.

Hoddeson:

As far as I can tell, we touched upon major papers. There are a few other summary papers that you wrote later on.

Wigner:

Yes. I wrote a paper together with Dr. Seitz, much later, but I don't remember it.

Hoddeson:

There's one on the effect of radiation in solids, [Seitz, S. and Wigner, E.P., "The Effects of Radiation on Solids," Scientific American, 195, pp. 76-84 (1965).] that appeared in Scientific American.

Seitz:

We also worked on one together in that series.

Wigner:

Yes.

Hoddeson:

— the Seitz-Turnbull series. That's a review paper, is it not?

Seitz:

Well, it's a kind of a —

Wigner:

It's a general treatment.

Hoddeson:

That's one of the wartime papers.

Wigner:

Yes.

Hoddeson:

Now, you were head of the Met Lab?

Wigner:

No, I was only head of the theoretical group.

Seitz:

The effect was sometimes called the Wigner disease.

Wigner:

Yes, which I am very much objecting to, because if you discover a new sugar and call it the Wigner Sugar, that's fine, but a disease shouldn't be called after me.

Hoddeson:

I was curious to get your reflections on — yes?

Wigner:

I think Dr. Seitz, Fred, contributed to it very much.

Seitz:

You were the one who pointed out that there was great danger, particularly in graphite. Then Szilard realized there was also the stored energy problem.

Wigner:

Right.

Seitz:

And that was the point at which I got into the act, and tried to do some experiments.

Wigner:

And you know who did the terrible experiments, the British, who had an accident as a result of it.

Hoddeson:

Did you do those experiments at Penn?

Seitz:

No, there was a group at Argonne Laboratories — I think it's probably mentioned in the Mott book — It was under James Franck and Milton Burton, who later went to Notre Dame.

Wigner:

Oh, yes.

Seitz:

We brought in Bob Maurer who did the very careful thermal release measurements.

Wigner:

Yes, and the British did, of course.

Seitz:

I don't know how much of this has ever seen the light of day, but there was quite a team at Argonne during the war, all working on these effects.

Hoddeson:

I think actually I've heard about some papers that are still at Argonne, on this subject, which I think I'll have to see if I can dig up.

Seitz:

It broke out, in a sense, after World War II, and people did more careful work on other things.

Hoddeson:

I gather, you learned things about solids from this.

Seitz:

We learned a good deal. Yes.

Hoddeson:

About, well, for example, it's hard to tell just from the SCIENTIFIC AMERICAN article, but about the arrangement and about the nature of the defects and the way they move around and so on.

Seitz:

That's right. Eugene was deeply involved in the theory of the reactor and the design in that period.

Wigner:

The nuclear reactor.

Seitz:

The nuclear reactor. He recognized the dangers that might occur from radiation damage. Then other people went to work on it in a quantitative sense.

Wigner:

Even Seaborg worked on it.

Seitz:

Seaborg was concerned.

Hoddeson:

Just thinking about the wartime contributions, I usually think about the contributions having been greatest in the semiconductor area, and in the area of producing techniques for studying solids, such as the resonance techniques. And also neutron diffraction.

Seitz:

That was important.

Hoddeson:

A very important one. And the low temperature machine, the Collins machine. How does this compare with those, in magnitude and influence?

Seitz:

Well, one learned a great deal about crystal defects, especially later on when people began to use gamma rays and electrons for very selective damage. The effects one had in the reactor were rather gross, because they were due to neutron bombardment. But the postwar work, stimulated by the wartime work, told us a great deal in a quantitative sense about the defects.

Hoddeson:

Do you think you would have learned the same things in other ways had the war not intervened?

Seitz:

Well, it accelerated it by years. You could also get money to do those experiments.

Wigner:

(Laughs) Yes.

Hoddeson:

Were there some other similar advantages for solid state research that came out of the work of the Metallurgical Laboratory, besides the ones we've mentioned?

Wigner:

Well, Dr. Seitz did a good deal of work on these defects, and that was very important also on the initiation of recovery from the defects, that if you heat it up the material it recovers, that is the defects disappear. And Fred made an estimate of how much heating is needed, and his estimate turned out to be quite close to the actual experimental value. Is that not right?

Seitz:

Yes, but then we had experiments.

Hoddeson:

Right. Have we touched upon the major places where you interacted with Seitz?

Wigner:

I think so.

Hoddeson:

Can you think of anything really important that I've left out that I might come back and discuss with you later?

Wigner:

Well, you know, my lectures on solid state physics I think were quite good.

Seitz:

They were excellent.

Wigner:

And informed many people of many parts of solid state physics, which was at that time difficult to find in books. Now, there are some very good books, in particular...

Seitz:

At least a dozen books now.

Wigner:

Well, yes. I still admire the one which I recommended to you, Fred Seitz's book.

Hoddeson:

Now, you gave a lecture course at Princeton in the early thirties?

Wigner:

Yes. Well, not so early, mid-thirties. And also, when I got back.

Hoddeson:

What level were these lectures on?

Wigner:

Oh, it assumed they were for graduate students. It assumed a certain knowledge of quantum mechanics. But you see, for instance, the fact that there are four kinds of solids, or if you want, five kinds of solids was rarely discussed by others, nor the question and why they are so different. You know, I've often mentioned that if I drop my keys — where are my keys?

Seitz:

In your topcoat.

Wigner:

If I drop my keys I don't worry at all whether they will be broken, but if I drop a cup or a glass, I worry at once, and usually it is broken. That is a very fundamental and noticeable difference. The explanation of these facts uses, to a very large extent, the basic fact that there are fundamental differences in the structures of different solids, that there are four types of solids.

Seitz:

The first series of lectures you gave in this country were in the autumn of 1932.

Wigner:

On solid-state physics.

Seitz:

I took the notes. That was one of the jobs we had as graduate students.

Hoddeson:

Do either of you have a copy of those notes some place? We would be very interested in these notes!

Seitz:

If I have them, they're stored at Lake George.

Wigner:

I may have them.

Seitz:

One of the troubles is, I stored all that stuff in the basement over at the campus, and we had a flood, and I don't know.

Wigner:

I may have it. But I am not sure, because I have a large stack of papers, which are lecture notes.

Hoddeson:

That would be very interesting to look at, to see how things were presented at that time. This, I gather, was one of the early courses, or perhaps the earliest course, in solid state in the United States.

Wigner:

That I don't know.

Seitz:

I'm sure it was.

Hoddeson:

Who else could have given it?

Seitz:

There were lectures in crystallography, but that's different.

Wigner:

Oh yes, that's very different.

Baym:

What was the course called?

Wigner:

On that I have amnesia.

Seitz:

It was probably, Solid State. Something simple like that.

Baym:

The name was used by then?

Seitz:

Oh yes. That went way back.

Seitz:

There were German books, Fust and Schuss that go back well into the twenties.

Wigner:

Is that so?

Seitz:

The chemists.

Wigner:

The chemists had books on it. Yes. Oh, that's right. Yes. (Noise of keys)

Baym:

Don't drop them.

Wigner:

But you see, that's really a remarkable difference, for instance (meaning, difference between keys and glasses)... and there are many similar differences. I wouldn't like to have sodium hydride in my pocket either.

Hoddeson:

How many students would come to this course?

Wigner:

It was the right number, about 15.

Hoddeson:

About 15?

Wigner:

Which I think is the right number, because if they don't understand it, or if you are not clear, they speak up. Now, when there are 50, they don't, they are embarrassed to speak up.

Seitz:

That, however, was about ten percent of the whole Princeton Graduate School.

Wigner:

Yes.

Seitz:

There were less than 150 students. There were chemists who came too. Princeton was very strong in physical chemistry.

Hoddeson:

So it was a mixture of physics students and chemistry students.

Wigner:

Physical chemists also. I also started as a physical chemist.

Hoddeson:

Well, it would be wonderful to see those lectures.

Wigner:

I will try to find them, but I will have to go back to Princeton to do that. And maybe I find them among my records.

Hoddeson:

I would very much appreciate your looking. One last question. Once, when I was reading through the 1932 or 1933 issue of the Bell Laboratories RECORD, I noticed that you gave a lecture at Bell on the applications of quantum mechanics to chemistry. I was wondering whether that was one of the talks that you were perhaps giving to various institutions?

Wigner:

No. No.

Hoddeson:

Do you remember that talk?

Wigner:

Well, no, I don't remember the talk, but I remember that I gave several talks, some talks at Bell Telephone Laboratories office, which was at that time —

Seitz:

On West Street, yes.

Wigner:

Yes, far downtown, West Street.

Seitz:

They had a regular colloquium. New Jersey was close so they would pay expenses to go to New York. But the Labs weren't anything like the national center they are now.

Hoddeson:

But they had very eminent people. I noticed that in that same period that you spoke, they had Louis de Broglie's brother, Maurice, and they had others of similar ilk.

Seitz:

Karl Darrow was the organizer of all these things in those days.

Wigner:

And he was very able. He knew many things. He was not so much contributing as knowing both people and subjects.

Hoddeson:

I gather that was a very interesting subject. Their colloquia I think were large meetings at that time.

Wigner:

Yes. Yes, they were large meetings.

Hoddeson:

And so they would have chosen a subject that had very wide interest, and that apparently was one.

Wigner:

You see, at that time, people's interest encompassed a larger fraction of physics than it does now. Much larger. At that time, we believed we knew physics. Now, we know we don't.

Seitz:

The specialization has gone about two notches down since then.

Hoddeson:

Where was the first notch?

Seitz:

Well, between pre and post World War II, people became much more specialized. And then in the intervening period, the last 20 years, there's been another level of specialization.

Hoddeson:

Thank you very much, both of you. It's been a pleasure.