On the spectrum of the Schrödinger operator with a constant magnetic field plus a decreasing radial potential
type: Item
instance of: scholarly article
title: On the spectrum of the Schrödinger operator with a constant magnetic field plus a decreasing radial potential
zbMATH Open document ID: 0916.35076
author: Mohamed Ali Tagmouti
published in: Journal of Functional Analysis
publication date: 1998-12-02T00:00:00Z
review text: The spectral problem for a class of 2-D Schrödinger operators with a constant magnetic field plus a decreasing radial potential is investigated. The spectrum consists of clusters of real positive eigenvalues which accumulate to zero. Asymptotic expansions of the eigenvalues are established and the coefficients of this expansion are related to a certain transformation of the potential. Explicit formulae for the Weinstein band invariants of cluster distribution measures are reported.
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 1213988
zbMATH Keywords: asymptotic expansions of the eigenvalues
zbMATH Keywords: clusters of real positive eigenvalues
zbMATH Keywords: Weinstein band invariants
reviewed by: Nikolai L. Vulchanov
MaRDI profile type: Publication
full work available at URL: jfan.1997.3242
OpenAlex ID: W2061671252
cites work: Schrödinger operators with magnetic fields. I: General interactions
cites work: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
cites work: Calcul fonctionnel à plusieurs variables pour des opérateurs pseudodifferentiels dans \(R^ n\)
cites work: Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
cites work: Inverse spectral problem for the 2-sphere Schrödinger operators with zonal potentials
cites work: Zonal Schrödinger operators on the \(n\)-sphere: Inverse spectral problem and rigidity
cites work: Q3810249
cites work: Proprietes asymptotiques du spectre dioperateurs pseuwdifferentiels sur IRn
cites work: The weyl calculus of pseudo-differential operators
cites work: Q4185363
cites work: Autour de l'approximation semi-classique. (Around semiclassical approximation)
cites work: Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold
cites work: Asymptotics of eigenvalue clusters for the Laplacian plus a potential
DOI: 10.1006/JFAN.1997.3242
Recommended article: Q4309705
Recommended article: On the spectrum of two-dimensional Schrödinger operators with spherically symmetric, radially periodic magnetic fields
Recommended article: The essential spectrum of Schrödinger operators with asymptotically constant magnetic fields on the Poincaré upper-half plane
Recommended article: Asymptotics of the infimum of the spectrum of Schrödinger operators with magnetic fields
Recommended article: The spectrum and the scattering problem for the Schrödinger operator in a magnetic field
Recommended article: On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov--Bohm magnetic field
Recommended article: Q5487700
Recommended article: Lower bounds for the spectra of Schrödinger operators with magnetic fields
Recommended article: The essential spectrum of two-dimensional Schrödinger operators with perturbed constant magnetic fields
Recommended article: Spectral asymptotics for magnetic Schrödinger operator with slowly varying potential
description: scientific article; zbMATH DE number 1213988