Recollections of solid state physics This seems relevant to another question on which my memory fails to serve namely when and how it was first realized that a filled band would give an insulator. In retrospect it seems to be an obvious consequence of the existence of bands, at least in the tight-binding limit, and particularly obvious from the arguments sketched above. It seems almost incredible that this point could have been missed but i have no clear recollection of when I became aware of it, and it is certainly not mentioned in any paper of that time This work was complete by the spring of 1929, and since at that time Heisenberg ent on sabbatical leave, i moved to Zurich to work with Pauli. here i left metals for a while, since Pauli suggested to me the problem of heat conduction in non- metallic crystals, under the influence of the anharmonic forces. This was a problem hich, at least at high temperatures, could be treated classically. Pauli had been interested in this problem and had looked at the related question of the absorption of sound waves because of anharmonicity. The abstract of a talk he gave to a meeting is published, ) and the answer given there is wrong (probably the only error in print under Paulis name) because it gives a finite damping in a linear chain, for hich in fact the three-phonon processes, which he was studying, do not occur He showed me a few pages of notes on this problem, to start me off. Apart from this guidance I looked at the problem from first principles, and this was probably fortunate, because there were a number of different wrong approaches in the literature, and it was less confusing to find the solution first, and then discover where others had gone wrong This led to the concept(and the ugly word) of Umklapp processes, and to the prediction of the exponential rise of the heat conductivity at low temperatures, (8) verified only in 1951 by Berman (9) In many ways my paper did not dispose of the problem. For example, it failed to point out that a pure substance, to show the exponential rise, had to be also isotopically pure. This omission made the experi mental discovery of the effect more difficult. Other, more sophisticated parts of the problem are still not completely sorted out. I submitted a thesis on this topi to leipzig(my one semester in Zurich not being an adequate residence qualification there)and returned to Zurich as Pauli s assistant I then started thinking further about electrons in metals. I felt uncomfortable about having, in my work on the Hall effect, relied on the flattening of the energy surface near the band edge, a result then known only in the tight-binding limit which was not realistic for conduction electrons. It seemed obvious that in the opposite limit of free electrons this effect was absent, and one therefore did not know what was happening in the intermediate case. It suddenly dawned on me that, if a weak potential was added as a small perturbation, there would be band gaps near the Bragg reflexions, and that the energy surface there had zero slope though, for a very weak potential this flattening was confined to a very narrow region near the edge, and the slope returned to its free-electron value more rapidl the weaker the potential(o) Few pieces of work have given me as much pleasure as this discovery, whichRecollections of solid state physics 31 This seems relevant to another question on which my memory fails to serve, namely when and how it was first realized that a filled band would give an insulator. In retrospect it seems to be an obvious consequence of the existence of bands, at least in the tight-binding limit, and particularly obvious from the arguments sketched above. It seems almost incredible that this point could have been missed, but I have no clear recollection of when I became aware of it, and it is certainly not mentioned in any paper of that time. This work was complete by the spring of 1929, and since at that time Heisenberg went on sabbatical leave, I moved to Zurich to work with Pauli. Here I left metals for a while, since Pauli suggested to me the problem of heat conduction in non￾metallic crystals, under the influence of the anharmonic forces. This was a problem which, at least at high temperatures, could be treated classically.Pauli had been interested in this problem and had looked at the related question of the absorption of sound waves because of anharmonicity. The abstract of a talk he gave to a meeting is published,(7) and the answer given there is wrong (probably the only error in print under Pauli's name) because it gives a finite damping in a linear chain, for which in fact the three-phonon processes, which he was studying, do not occur. He showed me a few pages of notes on this problem, to start me off. Apart from this guidance I looked at the problem from first principles, and this was probably fortunate, because there were a number of different wrong approaches in the literature, and it was less confusing to find the solution first, and then discover where others had gone wrong. This led to the concept (and the ugly word) of Umklapp processes, and to the prediction of the exponential rise of the heat conductivity at low temperatures,(8) verified only in 1951 by Berman.(9) In many ways my paper did not dispose of the problem. For example, it failed to point out that a 'pure' substance, to show the exponential rise, had to be also isotopic ally pure. This omission made the experi￾mental discovery of the effect more difficult., Other, more sophisticated parts of the problem are still not completely sorted out. I submitted a thesis on this topic to Leipzig (my one semester in Zurich not being an adequate residence qualification there) and returned to Zurich as Pauli's assistant. I then started thinking further about electrons in metals. I felt uncomfortable about having, in my work on the Hall effect, relied on the flattening of the energy surface near the band edge, a result then known only in the tight-binding limit, which was not realistic for conduction electrons. It seemed obvious that in the opposite limit of free electrons this effect was absent, and one therefore did not know what was happening in the intermediate case. It suddenly dawned on me that, if a weak potential was added as a small perturbation, there would be band gaps near the Bragg reflexions, and that the energy surface there had zero slope, though, for a very weak potential this flattening was confined to a very narrow region near the edge, and the slope returned to its free-electron value more rapidly the weaker the potentiaL<lO) Few pieces of work have given me as much pleasure as this discovery, which