Semiclassical analysis of discretizations of Schrödinger-type equations

Peter Markowich, Paola Pietra, Carsten Pohl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)397-413
Number of pages17
JournalVLSI Design
Volume9
Issue number4
StatePublished - Dec 1 1999

Keywords

  • Discretization of Schrödinger equation
  • Wigner transform

ASJC Scopus subject areas

  • Hardware and Architecture
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering

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