A finite-difference method for the numerical solution of the Schrödinger equation
type: Item
instance of: scholarly article
title: A finite-difference method for the numerical solution of the Schrödinger equation
zbMATH Open document ID: 0877.65054
DOI: 10.1016/S0377-0427(96)00156-2
author: P. S. Williams
author: T. E. Simos
published in: Journal of Computational and Applied Mathematics
publication date: 1997-12-10T00:00:00Z
review text: New finite difference methods are proposed for the numerical solution of the Schrödinger equation: \(y''(x)= [V(x)- E]y(x)\), where the potential \(V\) is a given function and \(E\) a real constant. The methods are symmetric four-step linear methods for special second-order equations whose coefficients have been suitably selected (for some type of potentials) taking into account not only the local discretization error but also the phase-lag and the interval of periodicity. In this way, the authors propose as optimal a sixth-order method with phase-lag of order eight. The paper includes also the results of some numerical experiments with different potentials in which to show the efficiency of the new method it is compared to an extended Numerov's method proposed by \textit{V. Fack} and \textit{G. Vanden Berghe} [J. Phys. A 20, 4153-4160 (1987; Zbl 0626.65079)].
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 1022218
zbMATH Keywords: finite difference methods
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: symmetric four-step linear methods
zbMATH Keywords: numerical experiments
reviewed by: Manuel Calvo
MaRDI profile type: Publication
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full work available at URL: s0377-0427(96)00156-2
OpenAlex ID: W2013349292
description: scientific article; zbMATH DE number 1022218