On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
type: Item
instance of: scholarly article
title: On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
zbMATH Open document ID: 0594.34022
DOI: 10.1007/BF01211761
author: Percy A. Deift
author: Rainer Hempel
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The model problem for the one-electron theory of solids for the Schrödinger operator \(H=-\Delta +V(x)\) of the pure crystal and for W(x) the potential which describes the ''impurity'' is considered. The problem under study is the following: given an energy \(E\in R(\sigma (H))\) (where \(\sigma\) (H) is the spectrum of H), does there exist a real coupling constant \(\lambda\) so that \(E\in \sigma (H-\lambda W)\). A number of results asserting the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap \(\sigma\) (H) are proved. The existence of these eigenvalues is an important element in the theory of the colour of crystals. The basic theorems are proved in \(R^ n\); stronger results for \(n=1\) are presented.
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 3955443
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: eigenvalues
zbMATH Keywords: colour of crystals
reviewed by: B. Konopelchenko
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01211761
OpenAlex ID: W1998873231
description: scientific article; zbMATH DE number 3955443