Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit

Peter A. Markowich*, Paola Pietra, Garsten Pohl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

80 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 test examples are presented to help interpret the theory.

Original languageEnglish (US)
Pages (from-to)595-630
Number of pages36
JournalNumerische Mathematik
Volume81
Issue number4
StatePublished - Feb 1999
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit'. Together they form a unique fingerprint.

Cite this