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 ei*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.
