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.
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Original Russian Text © A. V. Pereskokov, 2012, published in Matematicheskie Zametki, 2012, Vol. 92, No. 4, pp. 583–596.
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Pereskokov, A.V. Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators. Math Notes 92, 532–543 (2012). https://doi.org/10.1134/S0001434612090258
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DOI: https://doi.org/10.1134/S0001434612090258