Sharp exponential bounds on resonances states and width of resonances
type: Item
instance of: scholarly article
title: Sharp exponential bounds on resonances states and width of resonances
zbMATH Open document ID: 0652.47008
DOI: 10.1016/0196-8858(88)90011-5
published in: Advances in Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The paper is a contribution to a geometrical theory of resonances. It deals with potentials of certain geometrical shapes in the quasiclassical regime. The main result is the proof of existence of resonances and estimates of the width of resonances in terms of geodesic distances determined by the potential (instanton actions). The Agmon-type approach is used and a perturbative argument provides exponential bounds on the resonances states. These results are applied to the shape and Stark resonances and give a partial generalization of the classical Oppenheimer formula derived original for the hydrogen atom.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 46N99
zbMATH DE Number: 4063841
zbMATH Keywords: geometrical theory of resonances
zbMATH Keywords: existence of resonances
zbMATH Keywords: width of resonances
zbMATH Keywords: geodesic distances
zbMATH Keywords: instanton actions
zbMATH Keywords: Agmon-type approach
zbMATH Keywords: exponential bounds
zbMATH Keywords: Stark resonances
zbMATH Keywords: Oppenheimer formula
zbMATH Keywords: hydrogen atom
author: I. M. Sigal
reviewed by: Marco Codegone
MaRDI profile type: Publication
full work available at URL: 0196-8858(88)90011-5
OpenAlex ID: W2014492474
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description: scientific article; zbMATH DE number 4063841