- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
VLSI Design
Volume 9 (1999), Issue 4, Pages 397-413
doi: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.