A note on the eigenvalues of the Hamiltonian of the harmonic oscillator perturbed by the potential \(\lambda x^2/(1+gx^2)\)
type: Item
instance of: scholarly article
title: A note on the eigenvalues of the Hamiltonian of the harmonic oscillator perturbed by the potential \(\lambda x^2/(1+gx^2)\)
zbMATH Open document ID: 0891.34079
DOI: 10.1016/0034-4877(96)89768-0
author: Silvestro Fassari
published in: Reports on Mathematical Physics
publication date: 1998-08-03T00:00:00Z
review text: The author uses a perturbation argument for the Fredholm determinant of the Birman-Schwinger kernel of the operator \(H_0-{\lambda\over g(1+gx^2)}\), where \[ H_0= -{d^2\over dx^2}+ x^2, \] to determine the ground state energy and the first excited level energy of the Hamiltonian \[ H_0- {\lambda x^2\over(1+ gx^2)}= H_0-{\lambda\over g(1+ gx^2)}+ {\lambda\over g} \] in terms of smooth functions of the parameters \(\lambda\) and \(\eta= g^{-1/2}\) in a neighbourhood of \((0,0)\).
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 1090417
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: eigenvalues
zbMATH Keywords: Fredholm determinant
zbMATH Keywords: Birman-Schwinger kernel
zbMATH Keywords: Hamiltonian
reviewed by: W. D. Evans
MaRDI profile type: Publication
full work available at URL: 0034-4877(96)89768-0
OpenAlex ID: W2013337673
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description: scientific article; zbMATH DE number 1090417