Precise spectral asymptotics for perturbed magnetic Schrödinger operator
type: Item
instance of: scholarly article
title: Precise spectral asymptotics for perturbed magnetic Schrödinger operator
zbMATH Open document ID: 0872.35073
DOI: 10.1016/S0021-7824(97)89950-3
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1997-07-27T00:00:00Z
review text: For a Schrödinger operator \(H_B\) with a constant nondegenerate magnetic tensor \(B\), perturbed by an electric potential \(V\) decaying at infinity, two types of spectral asymptotics are considered: 1) a series of eigenvalues of \(H_B+ V\) in a gap of the essential spectrum \(\sigma_{\text{ess}}(H_B)\) of \(H_B\), and 2) the number of eigenvalue branches of a family \(H_B+tV\), crossing an energy level in a gap of \(\sigma_{\text{ess}}(H_B)\), as \(t\to+\infty\) (in the last case, \(V\) is assumed to be nonnegative). The principal terms of the asymptotics, with remainder estimates, which are in certain cases sharp, are computed; for the first problem, under additional conditions of global character, the next term of the asymptotics is computed.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 1022291
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: spectral asymptotics
zbMATH Keywords: remainder estimates
author: Svetlana Boyarchenko
author: Sergei Levendorskiĭ
MaRDI profile type: Publication
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full work available at URL: s0021-7824(97)89950-3
OpenAlex ID: W2056079250
description: scientific article; zbMATH DE number 1022291