Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique. (Semi-classical behaviour of the Schrödinger operator with periodic potential)
type: Item
instance of: scholarly article
title: Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique. (Semi-classical behaviour of the Schrödinger operator with periodic potential)
zbMATH Open document ID: 0662.35023
DOI: 10.1016/0022-1236(87)90082-6
author: A. Outassourt
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: The Schrödinger operator with a periodic potential is considered. Let V be a smooth periodic function, we study the semi-classical behavior for a continuum spectrum of \(-h^ 2\Delta +V\) (h\(\to 0)\). We are interested in localization and width of bands. We give the interaction matrix up to an exponentially small error, measured by Agmon's distance between the wells. A detailed investigation of the spectrum is made for the case where V has one nondegenerate minima per unit cell. We also investigate the spectral properties of \(-h^ 2\Delta +V+\Delta V,\) where \(\Delta\) V is a smooth positive perturbation with compact support.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 4082070
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: periodic potential
zbMATH Keywords: semi-classical behavior
zbMATH Keywords: continuum spectrum
zbMATH Keywords: localization
zbMATH Keywords: width of bands
zbMATH Keywords: interaction matrix
zbMATH Keywords: Agmon's distance
zbMATH Keywords: spectral properties
zbMATH Keywords: smooth positive perturbation
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90082-6
OpenAlex ID: W1989418344
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description: scientific article; zbMATH DE number 4082070