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An operator splitting method for the Wigner-Poisson problem. (English) Zbl 0860.65143
The problem of discretization of the Wigner equation and the Wigner-Poisson system is considered. The essential idea is to split the operator into two parts: $$A=-{\mathbf v}.\nabla$$ and $$B$$ a pseudodifferential operator. A discretization scheme is constructed consisting of two parts per step; the first part involves only $$A$$ and the second only $$B$$. Convergence properties are considered in addition to the implementation.

##### MSC:
 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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