L ETTE RS TO THE EDITOR Ck k, Ckyk, 2 k.'+13 (k. al equation: A k, '+8 (k„'+ k,') Ck k„ Ck k, 2 k„'+8 (k,'+ k, ') Ck„k, Ck ky ui' '+ k„') . .as a2 =E a2, .as. and the wave function is given by (2) ps, qt, los, qs being the p-like degenerate functions at the top of the valence band. The essential result of our investigation is that to obtain the level scheme with an external held one need only replace k, by (1/i) (8/c)x) — (e/hc)A, etc. , where A is the vector potential of the field, and regard the a; as functions of the coordinates. If there is any ambiguity in the order of two noncommuting factors, the symmetrized product is meant. If spin-orbit coupling is taken into account then, mltatis nsltaedhs, the identical prescription still applies. Just what matrix replaces that of Eq. (1) depends on which model of the band one chooses. Kittel's model, 4 which seems most reasonable at the present time, would lead to a four-by-four matrix, the elements of which are linear combinations of those of Eq. (1). The resulting system of coupled diQerential equations is at
Physical Review – American Physical Society (APS)
Published: Oct 15, 1954
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