Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids
type: Item
instance of: scholarly article
title: Semiclassical analysis of low lying eigenvalues. III: Width of the ground state band in strongly coupled solids
zbMATH Open document ID: 0596.35028
DOI: 10.1016/0003-4916(84)90125-8
published in: Annals of Physics
publication date: 1984-01-01T00:00:00Z
review text: [Part I, cf. Ann. Inst. Henri Poincaré, Phys. Théor. 38, 295-308 (1983; Zbl 0526.35027), Corrections ibid. 40, 224 (1984; Zbl 0537.35023).] Schrödinger operators with periodic potentials in the limit of strong coupling are analyzed. In particular it is shown that the width of the ground state band \(\Delta\) (\(\lambda)\) with coupling constants \(\lambda^ 2\) of the potential behaves like lim -\(\lambda\) \({}^{-1} \log \Delta (\lambda)\). The paper makes heavy use of earlier results of the same author.
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 3960050
zbMATH Keywords: leading asymptotics
zbMATH Keywords: double wells
zbMATH Keywords: Schrödinger operators with periodic potentials
zbMATH Keywords: strong coupling
zbMATH Keywords: ground state band
author: B. Simon
reviewed by: Heinz Siedentop
MaRDI profile type: Publication
full work available at URL: 0003-4916(84)90125-8
OpenAlex ID: W2034349984
cites work: Q3969238
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cites work: Semiclassical analysis of low lying eigenvalues. II: Tunneling
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description: scientific article; zbMATH DE number 3960050