Abstract
In this paper we consider eigenvalues asymptotics of the energy operator in one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator in this model can be reduced to a class of infinite Jacobi matrices. Discrete spectrum of this class of operators represents the perturbed spectrum of harmonic oscillator. The perturbation is an unbounded operator compact with respect to unperturbed one. We use slightly modified Janas-Naboko successive diagonalization approach and some new compactness criteria for infinite matrices. First two terms of eigenvalues asymptotics and the estimation of remainder are found.
Mathematics Subject Classification (2010). Primary 47A75; Secondary 47B36.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Basel
About this paper
Cite this paper
Yanovich, E.A. (2013). Asymptotics of Eigenvalues of an Energy Operator in a Problem of Quantum Physics. In: Janas, J., Kurasov, P., Laptev, A., Naboko, S. (eds) Operator Methods in Mathematical Physics. Operator Theory: Advances and Applications, vol 227. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0531-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0531-5_10
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0530-8
Online ISBN: 978-3-0348-0531-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)