The Wigner Equation

Authors: Ansgar Jüngel

Publish Date: 2009

Volume: , Issue: , Pages: 1-17

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Abstract

The quantum mechanical motion of an electron ensemble can be described by the Schrödinger or the densitymatrix formulation see Sect 101 There is an alternative description based on the quantumkinetic Wigner formalism which we present and discuss in this chapter There are two main reasons for using this framework in applications mostly for transient problems First the Wigner picture allows in contrast to Schrödinger models for a modeling of scattering phenomena in the form of a quantum Boltzmann equation Second the quantumkinetic framework makes it easier to formulate boundary conditions at the device contacts which may be inspired from classical kinetic considerations 1 In this chapter following 2 we formulate the quantum Liouville equation the quantum Vlasov equation and quantum Boltzmann models and discuss their relations to the classical kinetic equations introduced in Chaps 3 and 4

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