An Operator Splitting Method for the Wigner–Poisson Problem
Anton Arnold, Christian A. Ringhofer · SIAM Journal on Numerical Analysis · 1996
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.