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# Alfred Landé - Session II

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Interview of Alfred Landé by Thomas S. Kuhn and John Heilbron on 1962 March 6,

Niels Bohr Library & Archives, American Institute of Physics,

College Park, MD USA,

www.aip.org/history-programs/niels-bohr-library/oral-histories/4728-2

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### Abstract

This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Ernst Back, Niels Henrik David Bohr, Max Born, Constantin Caratheodory, Peter Josef William Debye, Paul Ehrenfest, Albert Einstein, Walther Gerlach, Samuel Abraham Goudsmit, Werner Heisenberg, Heinrich Mathias Konen, Peter Lertes, Fritz London, Erwin Madelung, Wolfgang Pauli, Max Planck, Erwin Schrodinger, Arnold Sommerfeld, Otto Stern, George Eugene Uhlenbeck; Artillerie Prufungs-Kommission, Universitat Gottingen, Universitat Marburg, Universitat Munchen, Universitat Tubingen.

### Kuhn:

Before we pick up some of the questions from yesterday, there was one thing I wanted to ask you about. You spoke yesterday of a time when you talked with Debye, who said, something to the effect that “Have you heard what Schrodinger is doing?”

### Lande:

Yes, and he said, “This of course will lead to nothing. It is an absolutely crazy idea.”

### Kuhn:

Somebody has told me a story of a seminar at which Schrodinger was describing the de Broglie paper, and Debye said, “If there are waves, there must be a wave equation.” And Schrodinger went back to work on the wave equation. Now these two stories could be compatible, of course; it all depends upon the tone of voice of the first remark in the seminar.

### Lande:

Yes, on which was said first, and exactly the timing. Just in this connection, let me say that Schrodinger for years was preparing himself for this wave attitude… I was told yesterday by Professor Lenzen, who spoke with Sommerfeld in 1923 when he was here, that Sommerfeld mentioned that the Compton effect is very bad for wave theory. Now Schrodinger had given, about that time, a pure wave explanation of the Compton effect, which is certainly a preparation for his whole wave attitude. According to Schrodinger, the Compton effect is a resonance effect of the incoming waves reflected from a periodic distribution of matter in space… This paper I always found very important. It is reported on in my book on quantum mechanics — the Pitman Publishing Company — where the whole first chapter is devoted to showing that whatever you explained in particle terms you also can explain in wave terms. Schrodinger then sat down and explained the Doppler effect in pure particle terms… Simply according to conservation of energy and momentum. Conservation of energy and momentum corresponds to phase relations of frequencies. Now I love to lecture about this I found this in older papers of Schrodinger, before 1926. This is just as important as a preparation for modern quantum theory as Duane’s demonstration that the interference effect of wave reflection from crystal can be explained in a purely particle manner. It’s just the counterpart of it. Now these things were very important for the history of quantum mechanics, although nobody remembers them now.

### Kuhn:

One of the things that both Mr. Heilbron and I have been much interested in was early atom models and the transitions between one type of model and another…

### Lande:

Well, Sommerfeld tried out a model in which the two orbits were perpendicular to each other and found that this is more stable energetically than when they are in the same plane. Then he apparently gave up this idea.

### Kuhn:

No one had tried to do spectroscopy with a model of any sort?

### Lande:

No. Perhaps Sommerfeld tried, but as far as I know this was a purely speculative approach. Maybe the first attempt to introduce two orbits which are not in the same plane is in this helium model of mine. You find long calculations printed here. These calculations certainly are not reliable. They were only attempts. Sommerfeld — this is just personal remembrance again — was very enthusiastic about this work. “This is really some progress in the explanation of the helium spectrum with these two ortho-and-para terms.” Then he gave my calculations to Pauli, who at that time was about 20 years old. Pauli went through them and found mistakes. Then Sommerfeld wrote me another letter, “Your idea might be quite right but your calculations are no good. And for that reason I cannot take your results up in my Atomic Structure and Spectral Lines.” … This was already one of the examples where Pauli was taken as super-authority on the papers of other people. You know in several other cases, he was a bit too critical. But already at the age of 20 he was an authority on exactness of calculations.

### Kuhn:

I wondered if we could get to the helium atom from some of the earlier work on spatial models…

### Lande:

I think the simple reason in going to the helium is that it only had two electrons, and offered the next simplest problem after hydrogen. There is no other explanation. The hydrogen was practically solved after Sommerfeld … and the next step had to be taken.

### Kuhn:

The helium model is a spatial model, but it’s not like the polyhedral model…

### Lande:

I think these polyhedral models were not set up for any spectroscopic purposes, but only to illustrate that there is a possibility of having models of cubic symmetry as required by Born. But this was without envisaging any spectroscopic consequences. So from there to the helium is simply a natural gap because it was a quite different problem… The only connection is that before that all the models tried out were in one plane. Born and I were in this whole atmosphere of spatial arrangements, so it was natural to try helium from this point of view. I think this is all. During the calculations of the helium energy levels I studied an astronomical book on precession. I forgot the name of this book — every astronomer should have it… It’s mainly about the precessional movements of the moon.

### Kuhn:

Was this Charlier’s book?

### Lande:

I think it was, yes. And from that to the vector model is only a small step. This is already a vector model — two axes precessing around their common resultant… But I think that this paper of mine here, “Eine Quantenregel fur die raumliche Orientierung von Elektronenringen” may be the first in which this model is used extensively.

### Heilbron:

The idea in that paper of quantizing the angular momenta is slightly different than the model of space quantization used in the earlier paper on the helium atom. In the Nachtrag to the paper on helium the energy is somehow quantized.

### Lande:

Well, the angular momentum always played the leading role in quantization, in Sommerfeld’s and Wilson’s quantum ru1e. This is much more important than the quantization of energy… [Further discussion directed toward this distinction is here omitted] According to this Nachtrag, it seems quite clear that it is quantization of the individual orbital momenta and also quantization of the resultant of the momenta according to equation 2. Here are the quantum numbers of the angular momenta, and the energies simply can be calculated as h times the precessional frequency. As I said before, your question: Which is primary, quantization of the angular momentum or that of the energy, cannot be answered. They both belong completely together, if you have the one, you have the other. And quantization of the angular momentum was done already in the original quantum conditions of Sommerfeld and Wilson. The strangest thing is that quantization of linear momentum, p=h/2 introduced by Duane in 1925 was completely ignored.

### Kuhn:

In the paper on the Quantenregel you speak of some change in the formulation being due to something that happened in the Munich seminar.

### Lande:

Now this was in 1919, I really don’t know what went on in this seminar. I have a dim recollection that I painted on the blackboard these figures. I apparently didn’t express myself quite clearly what these vectors meant. Then one of the members of the seminar said, “These are the mean angular momenta and these are the resulting angular momenta,” — something like that.

### Kuhn:

On the helium papers, to what extent in 1919 was it a problem for you to account not only for the difference between ortho- and para-helium, but also to get a multiple structure — the singlet and doublet. That is, as I remember the particular point you make in the second helium paper is that this accounts for the existence of the two sorts of helium; on the other hand, the problem of the multiplicity of the two sorts does not seem to be very much of an issue.

### Lande:

It was an issue, but one which could have been solved only after the first issue was clarified. You go step by step. The first step is what the reason for the difference between ortho- and para-helium, and these other questions are so difficult that you better shift them aside and don’t think about them.

### Heilbron:

There is a suggestion in one of those papers that it is a mutation that gives the —

### Lande:

Well, whether this is just a kind of excuse, I don’t know. This just doesn’t mean much. I simply thought this is too difficult, that one has to go step by step.

### Heilbron:

The reason that this is so interesting is that in the 1921 paper when you identified Sommerfeld’s inner quantum number with the total angular momentum, the inner quantum number had been used to distinguish the multiplet levels in the triplets. But in your helium paper you had used the total angular momentum to distinguish between the different systems of terms in helium.

### Lande:

This was a time in which it proved quite successful to introduce sets of quantum numbers, η and K, and R and so on, even without knowing what they meant. And giving them names like mner, rumpf, and so on. And one tried this and that, and it gradually became clearer that these quantum numbers could be associated with a vector model.

### Kuhn:

Well, do you know when you saw Sommerfeld’s 1920 paper — the one that does introduce the inner quantum number — and utilizes it to explain singlet, doublet, triplet structure?

### Lande:

No, I don’t.

### Kuhn:

If I am right, this is the same paper you referred to later in connection with the anomalous Zeeman effect.

### Lande:

When Sommerfeld wrote a paper every theoretical physicist read it, and thought about it.

### Kuhn:

How much role do you suppose models are playing, how seriously are people taking them? To what extent do they feel free really to just invent quantum numbers?

### Lande:

Models have always played a very important part in private thinking. Then when you write a paper, you emphasize only those things which are certain, namely the quantum numbers which help you to calculate something. And sometimes speak, and sometimes do not speak, about the models which have led you to these conclusions. Some people think more in models, and other people more in terms of mathematical symmetries, matrices… My case is only to think in models, certainly. I am not a mathematician. So far as I know, Max Born who is a really trained mathematician, has much more sense for mathematical simplicity and simple form structure as he showed by giving matrix form to Heisenberg’s wild ideas.

### Heilbron:

Do you recall by any chance what kind of model you were thinking of which helped get the g factor.

### Lande:

Oh yes, the g factor quite at the end of this whole vector business… The only model consideration in the case of the g factor was that there was something — the core — which had twice as much magnetic moment than it ought to have. Of course there were model considerations, the whole vector model is a model… This is here the first paper on the anomalous Zeeman effect, 1921. Here is already almost the whole story — the g factor is in it. Now if we go over from the helium atom to the Zeeman effect, then let’s do it a little bit more systematically. The anomalous Zeeman effect of course was a pebble in the shoe of every physicist at that time. Various attempts were made, first, to systematize the Zeeman effect — Preston’s rule and Runge’s rule. They all were purely concerned with the Zeeman types, which you photograph — that means with the Zeeman lines. And — this is historically very strange — although the combination principle — a spectral line is the difference of two spectral terms — was given around 1900 by Rydberg and Ritz, Sommerfeld applied this combination principle to the normal Zeeman effect many years later, in 1915. Then the matter slept again completely. Sommerfeld himself tried — and also wrote a very interesting paper on the anomalous Zeeman effect, again purely from the point of view of the spectral lines. And it took from 1900 to 1921 until someone had the idea there again to try the combination principle on the anomalous Zeeman effect. This was the strangest thing. This was the decisive step. All the rest — the g factor, the g formula — was a trifle after that. Everybody could — after he had this key to the Zeeman types as derived from Zeeman terms. All of them depended only on having the magnificent photograph of Back, who analyzed each term exactly — “This is 3/4 and this is 5/6 and this is 7/8” — with the greatest accuracy. This is very simple. I came to Tubingen… in October 1922. Back gave me his material, already evaluated, and two months later I had the g formula — in December 1922. This was very simple.

### Kuhn:

What data had you had before you came to Tubingen, because you got some g factor formulas already in the first 1921 paper.

### Lande:

what I had before was mainly Sommerfeld’s paper on the anomalous Zeeman effect. I don’t have a copy of it here, but he showed up more regularities than Runge and Preston together… I was in Frankfurt, and this paper interested me very much. I thought this must be valuable. I thought about this. I remember in 1920 it was at home during my Christmas vacation, in my home town with my parents, and I went to a movie. The movie apparently didn’t interest me as much as these problems; and when I came back from the movie, I had the idea to try the combination principle. It was just an idea out of nothing.

### Kuhn:

Doesn’t the Sommerfeld 1920 paper already start talking combination principles?

### Lande:

You see, two things were in my head, as I remember. First of all the vector model, which of course pertains only to the spectral energies and spectral terms; on the other hand, I had in my head the anomalous Zeeman types with their intrinsic regularities. But in some way these two things had to be combined, and it was just a flash. But the strange thing is that Sommerfeld, who also had exactly the same material, and had already written the paper about the normal Zeeman effect, from spectral terms, did not get this idea first. I think one of the reasons was that as always older people are driven to think in certain fixed lines, once and for all. They cannot get away from them. And I was rather ignorant of what could be done and what should be done…

### Heilbron:

It was the first time you had become deeply immersed in spectroscopic data and so forth?

### Lande:

I had studied before all this happened. During the time I worked on the helium spectrum — I had studied very thoroughly the book by Konen, Spectrum Lines, which gave all the material. Also you find all the deviations from the (Balmer) formula, and the whole material including the rules of the — was the Zeeman effect also included I am not sure. Anyway, all this is found in Konen’s book. I knew Konen quite well; he was Professor in Bonn, the successor of Kayser, the great — also a great spectroscopist. This work of Konen was completely in my head. I remember years later I met Konen and he said to me, “Well, my work is completely out of date and never had any use,” and I told him that all my work was completely based on reading his book very thoroughly. This gave him very great satisfaction. But to repeat once more, this one idea to apply the combination principle to solve the anomalous Zeeman effect riddle is the one essential step. Everything that came later is simply ordering the material which Back had all prepared. On the grounds of being able to predict the anomalous Zeeman effect before having seen it, and sending the result to Paschen — Paschen was so enthusiastic that he then called me to Tubingen as a professor in his Institute. And as soon as I was there, October 1921, the rest came quite naturally, step by step.

### Kuhn:

In that first 1921 paper, you write down formulas like: g equals 2k over m minus one, with a different expression for each term of a triplet level. To what extent is the model itself helping to lead you to these expressions, do you suppose, and to what extent are you now seeing these pretty much straight out of the data that Sommerfeld reported?

### Lande:

As far as I can remember these formulas were simply tried out to put in a little bit of a system. There are three g’s and what is their relation? Whenever you have three points on a line you can set up a formula. If you have 3 g’s you can describe them by one formula. And the same was done later with the general g factor… In between comes this 1922 paper, where the vector model is applied… I have completely forgotten about this, but it deals with a paper of Heisenberg in which he reduces the anomalous Zeeman effect to a few ground principles — ground assumptions. And these ground assumptions are, to say the least, very temporary. Later nobody thought of them. They are all assumed ad hoc, completely ad hoc. The half quantum numbers are due to a division between the atomic shell and the atomic core, and the atomic core does not contribute to the quantization in the magnetic field. As I read through this, these are completely wild assumptions, only to be made to the purpose of complying with the experimental facts. Later they were completely given up. They didn’t make any sense. But off the record, I want to say this is very characteristic of Heisenberg. When he found something very difficult he immediately said, “There is something fundamentally new involved.” Instead of trying to explain it in terms of ordinary physics as known at that time. And as history shows, he had very treat success with this attitude, but sometimes it misfired, as in this case.

### Kuhn:

Didn’t you after this paper find some aspects of his use of the Rumpf useful in your own vector model?

### Lande:

No. I had the vector model, in which there is the orbital angular momentum in one direction, the core momentum in another, which is already two. This first paper in 1921 on the g factor — the core momentum apparently showed anomaly… From the model, as this 1923 paper shows, if the R has double magnetic moment then the g factor should have been J^{2} + R^{2} - K^{2} / 2J^{2}. I remember that several times I had discussions with Back, and said, that he must have made a mistake in his Zeeman types. “They ought to contain not the fraction 5/6 but the fraction 7/8.” And Back refused this absolutely, and said, “You must be wrong, my figures are certainly correct.” And it took quite a struggle between me as a theorist and Back as an experimentalist to convince me that there must be some modification. And then finally I drew up this table here with my expected figures from the model — I had this model with the double magnetic moment already — with my expected pictures; and on another sheet I took Back’s figures. And then I compared Back’s with mine, and then I saw the correction is J^{2} minus 1/4. In this way I arrived at the correct g factor, which of course can be written in a more symmetric way, J times J plus 1, and so on. You see theoretical physics is just — in this case — all kinds of number mysteries, until finally you put some system in them.

### Kuhn:

In that first paper on the Zeeman effect in October you ask, “Now what can the g factor mean?” You discuss it in terms of an anomalous Larmor frequency and say something about an anomalous value of e/m. I take it that here e/m does mean charge to mass, that it doesn’t yet mean magneto mechanical ratio.

### Lande:

Yes, but it comes from that, because if you write down the magnetic moment of a rotating electron, e occurs in it of course. And if you divide it by the angular momentum, m occurs in it. And the other factors cancel out so you can say it reduces to an anomalous ratio of e/m.

### Kuhn:

The first paper includes references to other places where this effect shows up, for example the Einstein - de Haas experiment. Did the notion of an anomaly in this area seem particularly strange or bothersome to you?

### Lande:

Yes, everybody was bothered by this anomaly and had various wild ideas, speculations where it would come from. And the wildest one certainly was that the electron was spinning around its own axis.

### Kuhn:

When people talk about electron spin — this was true very shortly afterwards — everybody says: Abraham had, shown that a rotating charge would have a gyro-magnetic ratio twice that of the normal Larmor procession…

### Lande:

I never knew about it. I knew of another paper by Kramers, who showed, without any quantum mechanics that the g factor must be two for any system. This is a very interesting paper shortly before Dirac’s paper came out. He explained the g factor from very general points of view. For relativistic reasons there must be this ratio. And. this is historically very important… In this ratio the quantum h cancels out. Whenever you have a formula without h, you must be able to understand it from purely classical points of view.

### Kuhn:

Well of course the Abraham paper is a purely classical paper.

### Lande:

I didn’t know of Abraham’s paper. It must have been much earlier than Kramers’ paper, because Kramers’ paper was already written with a view on the g factor. There was no model involved at all, but simply there is magnetic moment. There is angular momentum. I cannot reproduce it now, but you must look this up. It is quoted in this book on mechanics.

### Kuhn:

Did your own attitude towards models change during the course of this work, from 1919 when you really began on the spatial atom, into 1923?

### Lande:

I constantly alternated-between rodq1 considerations and purely numerical considerations. I shifted around numbers and then afterwards thought, “What does it mean to the model? And particles?” As in this example of the ideal formula where J squared entered instead of J times J plus 1. By the way, the g formula was the first instance in which these products, J times J plus 1, or I called it J - 1/2 times J plus 1/2 — of course this is only a matter of numbering — occurred before the Schrodinger wave equation. And if a really trained mathematician had gotten to such a formula containing n times n minus 1, he would immediately have been reminded of the problem of the potential — the electric potential — in the Laplace equation in the case of spherical symmetry, where this n times n plus 1 occurs.

### Heilbron:

I wonder if we can go back to the inner quantum numbers for just a minute or two. The selection rules that were then available for the azimuthal quantum number were contradictory. The ones that Rubinowicz derived were different than the ones Bohr derived. There should not be a delta n=0 in the Bohr presentation, but it should occur according to Rubinowicz and Sommerfeld. I was wondering whether the difficulty in harmonizing those two different selection rules for the same quantum number had any role in your identification of Sommerfeld’s inner quantum number with the total angular momentum.

### Lande:

As far as I remember they did not play a role, but this came only afterwards. If you take the term analysis of the Zeeman type and write down these schemes here — [Lande here points to a schema in one of his papers] — either you combine rows which both have the same length, or the one is one more than the other, but never one that is two more than the other, or two less than the other. And from this fact then you can again ask, “What does this mean in terms of the model?” It means that there is a selection rule that this quantum number never can jump more than one. So it always goes hand in hand.

### Kuhn:

Then in your own case, the concern with selection rules came really only afterwards?

### Lande:

Yes, the selection rule came only after, and I think in my papers it also came only in the second part.

### Heilbron:

Do you recall whether there was general concern over the different selection rules that were obtained either by correspondence arguments or by some other analysis?

### Lande:

No, I don’t think so, because the general viewpoints for selection rules were already in Sommerfeld’s original paper, that in the normal Zeeman effect the quantum number m can only jump one step, never two steps. [A question about Lande’s note in Naturwissensch,(1923) on “Versagen der Mechanik …” revealed that he had entirely forgotten this paper, had omitted it from his bibliography and had no reprints.]

### Kuhn:

We’ll have to get out a copy of that paper.

### Lande:

Is it not in the Physikalische Zeitschrift — here: “Schwierigkeiten in der Quantumtheorie des —”… “Vortrag vom Deutschen Physikertag in Bonn,” 1923 – I remember giving this and my 10 minutes were over and the man had the bell in his hand. I simply wanted to talk on, and made myself very unpopular. [A discussion of the sense of crisis in physics before 1925 as expressed by some comments of Pauli in the Pauli Memorial Volume is here omitted.]