Asymptotics of spectral data of a harmonic oscillator perturbed by a potential
type: Item
instance of: scholarly article
title: Asymptotics of spectral data of a harmonic oscillator perturbed by a potential
zbMATH Open document ID: 1162.34068
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-08-18T00:00:00Z
review text: The author proves some results on the asymptotic behaviour of the eigenvalues, and the normalizing constants of the corresponding eigenfunctions, of the perturbed harmonic oscillator \[ -y''(x)+x^{2}y(x)+q(x)y(x), \] where \(q'(x)\), \(xq(x)\in L^{2}(\mathbb R)\). As shown by the author, \textit{P. Kargaev} and \textit{E. Korotyaev} [Commun. Math. Phys. 249, No.~1, 133--196 (2004; Zbl 1085.81055)], these results are important for solving the corresponding inverse spectral problem.
reviewed by: Alan L. Andrew
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 5312814
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenfunctions
zbMATH Keywords: asymptotics
zbMATH Keywords: harmonic oscillator
author: Dmitry Chelkak
MaRDI profile type: Publication
full work available at URL: s10958-005-0342-5
OpenAlex ID: W1998659021
cites work: The spectral class of the quantum-mechanical harmonic oscillator
cites work: Inverse problem for harmonic oscillator perturbed by potential, characterization
cites work: An inverse problem for an harmonic oscillator perturbed by potential: uniqueness
cites work: Q5728604
cites work: Q3324254
DOI: 10.1007/S10958-005-0342-5
description: scientific article; zbMATH DE number 5312814