The stability of the density of states of Schrödinger operator under very small perturbations
type: Item
instance of: scholarly article
title: The stability of the density of states of Schrödinger operator under very small perturbations
zbMATH Open document ID: 0685.35081
DOI: 10.1007/BF01235738
author: Werner Kirsch
published in: Integral Equations and Operator Theory
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Lambda_ L\) be a cube in \({\mathbb{R}}^ d\), \(d\geq 2\), of side legth L centered at the origin, \(H_ L\) be the restriction of the Schrödinger operator \(H=-\Delta +V_ 0\) to \(\Lambda_ L\), \(V_ L\) be a bounded non negative function with support in \(\Lambda_ L\). The behaviour of the function \(\phi_ L(E)=N(H_ L,E)-N(H_ L+V_ L,E)\) as \(L\to +\infty\) is considered, where N(A,E) denotes the number of eigenvalues of A not exceeding E.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 4122494
zbMATH Keywords: number of eigenvalues
MaRDI profile type: Publication
cites work: Small Perturbations and the Eigenvalues of the Laplacian on Large Bounded Domains
cites work: On the density of states of Schrodinger operators with a random potential
cites work: Q4185363
cites work: Schrödinger semigroups
cites work: Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
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description: scientific article; zbMATH DE number 4122494