The shooting method for solving eigenvalue problems
type: Item
instance of: scholarly article
title: The shooting method for solving eigenvalue problems
zbMATH Open document ID: 0863.65044
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-12-09T00:00:00Z
review text: The generalized eigenvalue problem \({d^2R\over dv^2}=Q(v,\lambda)R\), \(v\in (-\infty,\infty)\), \(\lambda\in [a,b]\) under a boundedness condition is considered. The main results concern a characterization of the eigenvalues. Let \(Z(\lambda)\) be the number of zeros of a solution bounded on \((0,\infty)\) for \(\lambda\in [a,b]\). The author proves that under certain conditions on \(Q\), \(Z(\lambda)\) is well defined, nondecreasing and \(\lambda\) is an eigenvalue iff it is a discontinuity of \(Z(\lambda)\). The obtained results give a theoretical basis for the shooting method for solving the eigenvalue problem. The author presents applications of the shooting method to the radial equation associated with the \(n\)-dimensional Schrödinger equation with spherically symmetric potential function.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 944363
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: shooting method
zbMATH Keywords: Schrödinger equation
author: Xi Chen
reviewed by: Teresa Regińska
MaRDI profile type: Publication
OpenAlex ID: W1998717149
DOI: 10.1006/JMAA.1996.0389
description: scientific article; zbMATH DE number 944363