HW-12 - Theory of Solids HW-12 Solution By Qifeng Shan...

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1 Theory of Solids HW-12 Solution By Qifeng Shan Ashcroft and Mermin’s book 16-1 Let h ( k ) be any one-electron property whose total density is , ) ( ) ( 4 3 k k k g h π d H (16.33) where g is the electronic distribution function. If, for example, h ( k ) is the electronic energy, ε (k), then H is the energy density u; if h ( k ) is the electronic charge, e, then H is the charge density, ρ . The value of the density H in the neighborhood of a point changes because electrons move into and out of the neighborhood, some as the result of the semiclassical equations of motion, and some as a result of collisions. The change in h due to collisions is coll 3 coll ) ( 4 t g h π d dt dH k k (16.34) (a) Show from (16.8) that (d H / d t ) coll vanishes provided that all collisions conserve h (i.e., provided that there is only scattering between levels k and k ’ with h ( k ) = h ( k ’)). (b) Show that if (16.8) is replaced by the relaxation-time approximation (16.9), then (d
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This note was uploaded on 10/04/2011 for the course PHYS 4720 taught by Professor Shan during the Fall '09 term at Rensselaer Polytechnic Institute.

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HW-12 - Theory of Solids HW-12 Solution By Qifeng Shan...

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