Resonance selection principle and low energy resonances for a radial Schrödinger operator with nearly Coulomb potential
type: Item
instance of: scholarly article
title: Resonance selection principle and low energy resonances for a radial Schrödinger operator with nearly Coulomb potential
zbMATH Open document ID: 0811.34073
author: Marianna A. Shubov
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-05-09T00:00:00Z
review text: This paper is devoted to the study of resonances for the radial Schrödinger operator with Coulomb potential perturbed by a compactly supported function. The resonances are defined as poles of an analytic continuation of the quadratic form of the resolvent. One of the main results of the paper is the statement that resonances can be described as roots of the Jost function, like in the non-Coulomb case. Using this result the author proves that all resonances split into infinite sequences of series (corresponding to different values of an angular momentum \(\ell)\) and zero cannot be a point of accumulation of resonances when \(\ell\) is fixed. In order to obtain these results the main tool are estimates for the regular and Jost solutions of the perturbed equation which are obtained from Volterra integral equations for these solutions.
reviewed by: Y.P.Mishev
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 566439
zbMATH Keywords: resonances
zbMATH Keywords: radial Schrödinger operator with Coulomb potential
zbMATH Keywords: Jost function
zbMATH Keywords: estimates
zbMATH Keywords: perturbed equation
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1047
OpenAlex ID: W2071723656
DOI: 10.1006/JMAA.1994.1047
Recommended article: Low-energy chain of resonances for three-dimensional Schrödinger operator with nearly Coulomb potential
Recommended article: The resonance selection principle for the three-dimensional Schrödinger operator
Recommended article: Resonance functions for radial Schrödinger operators
Recommended article: On radial Schrödinger operators with a Coulomb potential
Recommended article: Q3700173
Recommended article: Resonances for the radial Dirac operators
Recommended article: Resonances for a semi-classical Schrödinger operator near a non trapping energy level
Recommended article: On radial Schrödinger operators with a Coulomb potential: general boundary conditions
Recommended article: On spectral properties of the resonances for selected potential scattering systems
Recommended article: Q3743676
description: scientific article; zbMATH DE number 566439