Journal Article

Gauss–Hermite wave packet dynamics: convergence of the spectral and pseudo-spectral approximation

Erwan Faou and Vasile Gradinaru

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 4, pages 1023-1045
Published in print October 2009 | ISSN: 0272-4979
Published online November 2008 | e-ISSN: 1464-3642 | DOI:

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The time-dependent linear Schrödinger equation for nuclei on the whole space is semidiscretized using Hermite and Gauss–Hermite basis functions. These are well suited, on the one hand, for the conservation properties of the numerical solution and, on the other hand, for their remarkable approximation properties. We investigate theoretically and numerically the convergence of the spectral and pseudo-spectral Gauss–Hermite semidiscretization schemes.

Keywords: Schrödinger equation; Gauss–Hermite approximation; spectral and pseudo-spectral methods

Journal Article.  0 words. 

Subjects: Mathematics