This article is cited in 7 papers

Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators

A. V. Pereskokov

Moscow Power Engineering Institute (Technical University)

Abstract: The eigenvalue problem for the perturbed resonant oscillator is considered. A method for constructing asymptotic solutions near the boundaries of spectral clusters using a new integral representation is proposed. The problem of calculating the averaged values of differential operators on solutions near the cluster boundaries is studied.

Keywords: spectral cluster, resonance, operator averaging method, coherent transform, WKB-approximation, turning point.

UDC: 517.958:530.145.6

Received: 13.03.2011

DOI: 10.4213/mzm9067

 English version: Mathematical Notes, 2012, 92:4, 532–543

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