On the eigenvalues of the perturbed Schrödinger operator with irrational magnetic flow
type: Item
instance of: scholarly article
title: On the eigenvalues of the perturbed Schrödinger operator with irrational magnetic flow
zbMATH Open document ID: 0830.35109
DOI: 10.1007/BF01076501
publication date: 1995-09-27T00:00:00Z
review text: We describe an approach to the eigenfunction problem for the perturbed Schrödinger operator \[ \left( i{ \partial \over \partial x} + 2 \pi \theta y \right)^2 - {\partial^2 \over \partial y^2} + V(x,y) \] with irrational magnetic flow and with a doubly periodic perturbation \(V(x,y) = V(x + 1, y) = V(x,y + 1)\). The approach is based on the representation of this operator as an operator in a Hilbert module over the \(C^*\)-algebra \(A_\theta\).
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 795619
zbMATH Keywords: perturbed Schrödinger operator
zbMATH Keywords: irrational magnetic flow
zbMATH Keywords: doubly periodic perturbation
author: Vladimir M. Manuilov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01076501
OpenAlex ID: W2008967267
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 795619