A spectral method for Schrödinger equations with smooth confinement potentials
type: Item
instance of: scholarly article
title: A spectral method for Schrödinger equations with smooth confinement potentials
zbMATH Open document ID: 1255.65218
author: Jerry Gagelman
author: Harry Yserentant
published in: Numerische Mathematik
publication date: 2012-10-22T00:00:00Z
review text: The expansion of the eigenfunctions of Schrödinger operators with smooth confinement potentials in Hermite functionsis studied; confinement potentials are potentials that become unbounded at infinity. The key result is that such eigenfunctions and all their derivatives decay more rapidly than any exponential function under some mild growth conditions to the potential and its derivatives. Their expansion in Hermite functions converges therefore very fast, super-algebraically.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P10
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6097146
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: eigenfunction expansion
zbMATH Keywords: smooth confinement potential
zbMATH Keywords: Hermite function
describes a project that uses: MPFR
describes a project that uses: TNT
describes a project that uses: Digital Library of Mathematical Functions
MaRDI profile type: Publication
full work available at URL: s00211-012-0458-8
OpenAlex ID: W2039140382
cites work: Q3969238
cites work: Practical quantum mechanics. Translated from the German.
cites work: MPFR
cites work: Q3579593
cites work: Regularity and approximability of electronic wave functions
DOI: 10.1007/S00211-012-0458-8
description: scientific article; zbMATH DE number 6097146