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IMA Journal of Numerical Analysis Advance Access published online on November 20, 2008
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn041
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Erwan Faou{dagger}

INRIA, ENS Cachan Bretagne, Avenue Robert Schumann F-35170 Bruz, France

Vasile Gradinaru

Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany

{dagger} Email: erwan.faou{at}irisa.fr

Received on 29 January 2007. Accepted for publication 14 February 2008.


  Abstract

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.

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


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