Geodesic
Asymptotics of the spectrum and quantum averages of a~perturbed resonant oscillator near the boundaries of spectral clusters
Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 163-210

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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.
Keywords: operator averaging method, coherent transform, WKB-approximation, turning point, spectral cluster. 
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     author = {A. V. Pereskokov},
     title = {Asymptotics of the spectrum and quantum averages of a~perturbed resonant oscillator near the boundaries of spectral clusters},
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A. V. Pereskokov. Asymptotics of the spectrum and quantum averages of a~perturbed resonant oscillator near the boundaries of spectral clusters. Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 163-210. http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a7/