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Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation

Erwan Faou 1, 2 Vasile Gradinaru 3
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : The time dependent linear Schrödinger equation for nuclei on the whole space is semi-discretised 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 semi-discretisation schemes. Schrödinger equation, Gauss- Hermite approximation, spectral and pseudo-spectral methods
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https://hal.inria.fr/hal-00777661
Contributor : Erwan Faou <>
Submitted on : Thursday, January 17, 2013 - 5:16:57 PM
Last modification on : Friday, February 5, 2021 - 3:49:12 AM

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  • HAL Id : hal-00777661, version 1

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Erwan Faou, Vasile Gradinaru. Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2009, 29, pp.1023-1045. ⟨hal-00777661⟩

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