Multiplicities of the eigenvalues of the Schrödinger equation in any dimension
type: Item
instance of: scholarly article
title: Multiplicities of the eigenvalues of the Schrödinger equation in any dimension
zbMATH Open document ID: 0647.35017
DOI: 10.1016/0022-1236(88)90091-2
author: T. Kappeler
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: We consider the Schrödinger equation on a bounded region \(D\subseteq {\mathbb{R}}^ d\) with Dirichlet boundary conditions \(-\Delta u+qu=\lambda u\), \(u|_{\partial D}=0\); here q is an element in \(L^{\infty}_{{\mathbb{R}}}(D)\) and the boundary \(\partial D\) of D is sufficiently smooth. We prove that the set Q of all potentials q in \(L^{\infty}_{{\mathbb{R}}}(D)\) which have the property that the equations above have at least one multiple eigenvalue is of first category.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 4056141
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: multiple eigenvalue
zbMATH Keywords: first category
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90091-2
OpenAlex ID: W2067450273
cites work: Genericity of Simple Eigenvalues for Elliptic PDE's
cites work: Modes and quasimodes
cites work: Multiplicities of the Eigenvalues of the Discrete Schrodinger Equation in any Dimension
cites work: Eigenfunctions and nodal sets
cites work: Q4040640
cites work: Q4110164
cites work: Unique continuation in geometry
cites work: Q5642974
cites work: Perturbazione dello spettro di un operatore ellittico di tipo variazionale, in relazione ad una variazione del campo
cites work: Q5614140
cites work: Generic Properties of Eigenfunctions
description: scientific article; zbMATH DE number 4056141