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A Wigner‐function approach to (semi)classical limits: Electrons in a periodic potential
Journal article   Peer reviewed

A Wigner‐function approach to (semi)classical limits: Electrons in a periodic potential

P. A. Markowich, N. J. Mauser and F. Poupaud
Journal of mathematical physics, Vol.35(3), pp.1066-1094
01/03/1994
DOI: https://doi.org/10.1063/1.530629

Abstract

SEMICLASSICAL APPROXIMATION BOLTZMANN−VLASOV EQUATION POTENTIAL ENERGY SEMICONDUCTOR DEVICES SCHROEDINGER EQUATION ELECTRONS PERIODIC VARIATIONS WIGNER DISTRIBUTION BAND STRUCTURE CRYSTAL LATTICES
A rigorous derivation of the semiclassical Liouville equation for electrons which move in a crystal lattice (without the influence of an external field) is presented herein. The approach is based on carrying out the semiclassical limit in the band‐structure Wigner equation. The semiclassical macroscopic densities are also obtained as limits of the corresponding quantum quantities.

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