We apply Wigner-transform techniques to the analysis of difference methods for Schroedinger-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.
|Number of pages
|Published - 1999
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Hardware and Architecture
- Computer Graphics and Computer-Aided Design