A new variable step method for the numerical integration of the one- dimensional Schrödinger equation
type: Item
instance of: scholarly article
title: A new variable step method for the numerical integration of the one- dimensional Schrödinger equation
zbMATH Open document ID: 0654.65064
DOI: 10.1016/0021-9991(88)90180-5
author: Hafez Kobeissi
author: Majida Kobeissi
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: A new variable step method is presented for the numerical integration of the one-dimensional Schrödinger equation of the form \[ y''(r)=(U(r)- E)y(r)=f(r)y(r) \] with the boundary condition \(y(0)=0\), \(\lim_{r\to \infty}y(r)=0\) and the continuity condition for y(r) and y'(r) at any arbitrary point \(r_ 0\), \(0<r_ 0<+\infty\), where U(r) is a given potential function, r is the internuclear distance. The authors were inspired by the work of \textit{A. D. Raptis} and \textit{J. R. Cash} [Comput. Phys. Commun. 36, 113-119 (1985; Zbl 0578.65086)]. This variable step method makes use of the ``canonical functions'' approach. At each interval, an estimate of the step-size h is determined in order to obtain the desired local accuracy. For the practical case of a given potential function with polynomial function with polynomial interpolations, the step-size h is directly given by a simple formula. The method is applied to the Morse potential function and numerical examples are presented.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 4068200
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: variable step method
zbMATH Keywords: Morse potential function
zbMATH Keywords: numerical examples
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90180-5
OpenAlex ID: W2028626995
cites work: An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
cites work: Q3231529
cites work: A variable step method for the numerical integration of the one- dimensional Schrödinger equation
cites work: The calculation of potential-energy curves from band-spectroscopic data
cites work: On testing diatomic vibration-rotation wavefunction for high levels
description: scientific article; zbMATH DE number 4068200