The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator \(H-\lambda W\) in a gap of \(H\)
type: Item
instance of: scholarly article
title: The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator \(H-\lambda W\) in a gap of \(H\)
zbMATH Open document ID: 0870.35073
DOI: 10.1007/PL00004573
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174941
review text: Let \(H\) be a Schrödinger operator with a uniform magnetic and bounded electric potential such that \(\sigma(H)\) has gaps, and let \(E\) be in a gap. Let \(W\geq 0\) be a potential decaying at infinity. In this paper, the asymptotics as \(\lambda\to+\infty\), of the numbers \(N_{\pm}(\lambda; H-E;W)\) of the eigenvalue branches of families \(H\mp\lambda W\) crossing an energy level \(E\) is computed. For \(+\) sign, the case of \(W\) decaying as \(|x|^{-2}\) or slowly is considered, for \(-\) sign, any polynomial decay is admissible.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 1028273
zbMATH Keywords: eigenvalue branches
zbMATH Keywords: crossing an energy level
author: Sergei Levendorskiĭ
MaRDI profile type: Publication
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OpenAlex ID: W4244615277
description: scientific article; zbMATH DE number 1028273