VLSI Design

VLSI Design / 1999 / Article
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International Workshop on Quantum Theory

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Volume 9 |Article ID 042190 | https://doi.org/10.1155/1999/42190

Peter A. Markowich, Paola Pietra, Carsten Pohl, "Semiclassical Analysis of Discretizations of Schrödinger-type Equations", VLSI Design, vol. 9, Article ID 042190, 17 pages, 1999. https://doi.org/10.1155/1999/42190

Semiclassical Analysis of Discretizations of Schrödinger-type Equations

Received13 Aug 1997
Revised01 Dec 1998

Abstract

We apply Wigner-transform techniques to the analysis of difference methods for Schrödinger-type equations in the case of a small Planck constant. In this way we are able to obtain sharp conditions on the spatial-temporal grid which guarantee convergence for average values of observables as the Planck constant tends to zero. The theory developed in this paper is not based on local and global error estimates and does not depend on whether caustics develop or not.Numerical examples are presented to help interpret the theory.

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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