An Operator Splitting Method for the Wigner–Poisson Problem
Abstract
The Wigner–Poisson equation describes the quantum-mechanical motion of electrons in a self-consistent electrostatic field. The equation consists of a transport term and a non-linear pseudodifferential operator. In this paper we analyze an operator splitting method for the linear Wigner equation and the coupled Wigner–Poisson problem. For this semidiscretization in time, consistency and nonlinear stability are established in an $L^2 $-framework. We present a numerical example to illustrate the method.
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Published In
SIAM Journal on Numerical Analysis
Pages: 1622 - 1643
ISSN (online): 1095-7170
Copyright
Copyright © 1996 Society for Industrial and Applied Mathematics.
History
Submitted: 14 October 1992
Accepted: 20 October 1994
Published online: 12 July 2006
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