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In this paper we consider eigenvalues asymptotics of the energy operator inthe one of the most interesting models of quantum physics, describing aninteraction between two-level system and harmonic oscillator. The energyoperator of this model can be reduced to some class of infinite Jacobimatrices. Discrete spectrum of this class of operators represents the perturbedspectrum of harmonic oscillator. The perturbation is an unbounded operatorcompact with respect to unperturbed one. We use slightly modified Janas-Nabokosuccessive diagonalization approach and some new compactness criteria forinfinite matrices. Two first terms of eigenvalues asymptotics and theestimation of remainder are found.

Asymptotics of eigenvalues for an energy operator of the one model of quantum physics