Geodesic
Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 583-596

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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. 
@article{MZM_2012_92_4_a8,
     author = {A. V. Pereskokov},
     title = {Asymptotics of the {Spectrum} and {Quantum} {Averages} near the {Boundaries} of {Spectral} {Clusters} for {Perturbed} {Two-Dimensional} {Oscillators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {583--596},
     publisher = {mathdoc},
     volume = {92},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a8/}
}
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A. V. Pereskokov. Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 583-596. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a8/