An operator splitting method for the Wigner-Poisson problem

Anton Arnold, Christian Ringhofer

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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 L2-framework. We present a numerical example to illustrate the method.

Original languageEnglish (US)
Pages (from-to)1622-1643
Number of pages22
JournalSIAM Journal on Numerical Analysis
Issue number4
StatePublished - Aug 1996


  • Operator splitting methods
  • Wigner functions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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