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Work on beta radioactivity

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Work on ferromagnetism and the 'Bethe Ansatz'

Hans Bethe
Scientist

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Ferromagnetism had interested me greatly. Heisenberg had made a theory of it in which his main point was that the exchange interaction between neighboring atoms must be attractive. But it was a rather phenomenological theory, and I wanted to do it better. There was the Ising theory which... of a linear chain of atoms which was purely classical. But I knew very well that electrons have spin, and in fact it was the spin of electrons which was important for making ferromagnetism, and so I decided already at Rome in the spring of '32 to make a quantum theory of... of ferromagnetism, I hoped. So I considered again a linear change, just like Ising had, but I treated the spin exchange properly by quantum mechanics, spin being a non-commuting variable. And I found the solution. I made an Ansatz, which is now known as the Bethe Ansatz, that you get product of functions, each function being e^{i*delta} where delta is the phase shift of the two electron wave function as you go from one atom to the next. So in terms of that phase shift I could write down the wave function of the entire chain, using a Slater Determinant and calculate the energy levels, and as expected at low energy I would get ferromagnetism. And you can just as easily do it for antiferromagnetism where you have repulsive interaction between neighboring spins; and then at higher temperature the order gets less and finally you get a Curie point and you get... you get only paramagnetism instead of ferromagnetism. And on the basis of this I was invited to a conference on ferromagnetism at Leipzig, I think it was April '33.

[Q] *'34... oh '33*.

'33 definitely.

[Q] *And so you went...*

Now this paper of mine, the so-called Bethe Ansatz, has been very much used in condensed matter physics and I haven't the slightest idea what people did with it. In fact from time to time I listened to a talk about it, as I did a year and a half ago, and what people have made of it seems to be totally unrelated to my original paper, but they claim that the Bethe Ansatz was important for their work.

The late German-American physicist Hans Bethe once described himself as *the H-bomb's midwife*. He left Nazi Germany in 1933, after which he helped develop the first atomic bomb, won the Nobel Prize in Physics in 1967 for his contribution to the theory of nuclear reactions, advocated tighter controls over nuclear weapons and campaigned vigorously for the peaceful use of nuclear energy.

**Title: **Work on ferromagnetism and the 'Bethe Ansatz'

**Listeners:**
Sam Schweber

Silvan Sam Schweber is the Koret Professor of the History of Ideas and Professor of Physics at Brandeis University, and a Faculty Associate in the Department of the History of Science at Harvard University. He is the author of a history of the development of quantum electro mechanics, "QED and the men who made it", and has recently completed a biography of Hans Bethe and the history of nuclear weapons development, "In the Shadow of the Bomb: Oppenheimer, Bethe, and the Moral Responsibility of the Scientist" (Princeton University Press, 2000).

**Tags:**
Werner Heisenberg

**Duration:**
4 minutes, 18 seconds

**Date story recorded:**
December 1996

**Date story went live:**
24 January 2008