Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons
type: Item
instance of: scholarly article
title: Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons
zbMATH Open document ID: 0667.46049
DOI: 10.1016/0022-247X(89)90108-X
author: Asao Arai
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: We analyze the spectral property of the Hamiltonian for a model of a quantum harmonic oscillator interacting with infinitely many scalar bosons. The Hamiltonian gives an example of perturbation problem of embedded eigenvalues with infinite dimensional Schrödinger's type operators. It is shown explicitly that the embedded eigenvalues of the free (unperturbed) Hamiltonian do not always disappear under the interaction (perturbation) and the disappearance or the stability of the embedded eigenvalues depends on the parameters contained in the Hamiltonian.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 4092151
zbMATH Keywords: model of a quantum harmonic oscillator interacting with infinitely many scalar bosons
zbMATH Keywords: perturbation problem of embedded eigenvalues with infinite dimensional Schrödinger's type operators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4092151