Asymptotics of the spectrum and quantum averages of a~perturbed resonant oscillator near the boundaries of spectral clusters

A. V. Pereskokov

Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 163-210.

Résumé

In the eigenvalue problem for a perturbed two-dimensional oscillator, we suggest a method for constructing asymptotic solutions near the boundaries of spectral clusters by means of a new integral representation and study the issue of calculating the average values of differential operators on the solutions near the boundaries of the clusters.

Détail

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

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