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VLSI Design
Volume 9 (1999), Issue 4, Pages 397-413
http://dx.doi.org/10.1155/1999/42190

Semiclassical Analysis of Discretizations of Schrödinger-type Equations

1Johannes Kepler Universität Linz, Institut für Analysis und Numerik, Abtl. Differentialgleichungen, Altenberger Str. 69, Linz A-4040, Australia
2Istituto di Analisi Numerica del C. N. R., Via Abbiategrasso 209, Pavia I-27100, Italy

Received 13 August 1997; Revised 1 December 1998

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.

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.