### 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.

Original language | English (US) |
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Pages (from-to) | 1622-1643 |

Number of pages | 22 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 33 |

Issue number | 4 |

State | Published - Aug 1996 |

### Fingerprint

### Keywords

- Operator splitting methods
- Wigner functions

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*33*(4), 1622-1643.

**An operator splitting method for the Wigner-Poisson problem.** / Arnold, Anton; Ringhofer, Christian.

Research output: Contribution to journal › Article

*SIAM Journal on Numerical Analysis*, vol. 33, no. 4, pp. 1622-1643.

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TY - JOUR

T1 - An operator splitting method for the Wigner-Poisson problem

AU - Arnold, Anton

AU - Ringhofer, Christian

PY - 1996/8

Y1 - 1996/8

N2 - 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.

AB - 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.

KW - Operator splitting methods

KW - Wigner functions

UR - http://www.scopus.com/inward/record.url?scp=0001720141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001720141&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001720141

VL - 33

SP - 1622

EP - 1643

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 4

ER -