R. E. Peierls this, but it did not occur to me to refuse, and I did my best. But, more relevant to the present story, he also introduced me to one of his research students, W.H MoCrea(now a distinguished astrophysicist), who was also thinking about con ductivity using what he and Fowler called the Heitler-London model. Actually this 4)was a one-electron tight-binding model with two centres of for On my return to Leipzig the project was abandoned, and Heisenberg suggested I looked at the‘ anomalous’,ic itive, Hall effect. i tackled this on the basis of Bloch' s theory of electrons in periodic fields, and first had to convince myself that the effect of the magnetic field on the wave vector of the electron was the same as for a free electron of the same velocity, but that the mean velocity of the electron same k, if the energy function E(k) different. It was obvious, in particulAr was given by dE/dk, and therefore different from that for a free electron of the that in Bloch' s tight-binding model the energy would flatten off near the band edge, so that the current would there go to zero. Thus for an electron near the band edge an electric field could cause a decrease, rather than an increase, in the velocity in the field direction. One's first shock on seeing this result is the fear that it might lead to a negative conductivity. One soon realizes, however, that for an ensemble of electrons in statistical equilibrium the positive acceleration of the electrons near the bottom of the band outweighs the negative acceleration of those near the top until for a full band the current just vanishes t this point one was close to an explanation of the positive Hall effect, subject only to the proof that the rate of change of the wavevector in the magnetic field is still given by the Lorentz force. At this point I cheated a little by disregarding inter-band terms, which for the purpose in hand were unimportant, but in other problems can cause headaches So the explanation of the positive Hall effect came out without much difficulty. I recall a comment by Heisenberg that this was similar to the situation in atomic spectra(pointed out, I think, by Pauli)where an atom with one, or a few, electrons missing from a closed shell was dynamically similar to one with just one, or a few electrons in that shell, except for some signs. My memory is confused, however, on the question whether this comment was made when Heisenberg suggested the problem to me, or when I showed him the answer. In other words, I am not clear whether Heisenberg had, with his usual powerful intuition, guessed in advance how the solution would come out. I reported previously that he had, but I am now rather doubtful whether this was right In any event it was gratifying to have solved one of the remaining mysteries I wrote a paper on the subject, 5)which was not too clearly written, and also gave a talk to a conference, of which a summary is published. (6)It contains a sketch the Fermi surface for a two-dimensional square lattice for the case of an almost empty, and an almost full band with tight binding. In the latter case the boundar consists of circular quadrants inside the four corners of the square which forms the Brillouin zone for that case. In the longer paper there is also the remark that the conductivity vanishes for a full band30 R. E. Peierls this, but it did not occur to me to refuse, and I did my best. But, more relevant to the present story, he also introduced me to one of his research students, W. H. McCrea (now a distinguished astrophysicist), who was also thinking about con￾ductivity using what he and Fowler called the Heitler-London model. Actually this(4) was a one-electron tight-binding model with two centres of force. On my return to Leipzig the project was abandoned, and Heisenberg suggested I looked at the' anomalous', i.e. positive, Hall effect. I tackled this on the basis of Bloch's theory of electrons in periodic fields, and first had to convince myself that the effect of the magnetic field on the wave vector of the electron was the same as for a free electron of the same velocity, but that the mean velocity of the electron was given by dE jdk, and therefore different from that for a free electron of the same k, if the energy function E(k) was different. It was obvious, in particular, that in Bloch's tight-binding model the energy would flatten off near the band edge, so that the current would there go to zero. Thus for an electron near the band edge an electric field could cause a decrease, rather than an increase, in the velocity in the field direction. One's first shock on seeing this result is the fear that it might lead to a negative conductivity. One soon realizes, however, that for an ensemble of electrons in statistical equilibrium the positive acceleration of the electrons near the bottom of the band outweighs the negative acceleration of those near the top, until for a full band the current just vanishes. At this point one was close to an explanation of the positive Hall effect, subject only to the proof that the rate of change of the wavevector in the magnetic field is still given by the Lorentz force. At this point I cheated a little by disregarding inter-band terms, which for the purpose in hand were unimportant, but in other problems can cause headaches. So the explanation of the positive Hall effect came out without much difficulty. I recall a comment by Heisenberg that this was similar to the situation in atomic spectra (pointed out, I think, by Pauli) where an atom with one, or a few, electrons missing from a closed shell was dynamically similar to one with just one, or a few, electrons in that shell, except for some signs. My memory is confused, however, on the question whether this comment was made when Heisenberg suggested the problem to me, or when I showed him the answer. In other words, I am not clear whether Heisenberg had, with his usual powerful intuition, guessed in advance how the solution would come out. I reported previously that he had, but I am now rather doubtful whether this was right. In any event it was gratifying to have solved one of the remaining mysteries. I wrote a paper on the subject,(5) which was not too clearly written, and also gave a talk to a conference, of which a summary is published.(6) It contains a sketch of the Fermi surface for a two-dimensional square lattice for the case of an almost empty, and an almost full band with tight binding. In the latter case the boundary consists of circular quadrants inside the four corners of the square which forms the Brillouin zone for that case. In the longer paper there is also the remark that the conductivity vanishes for a full band