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Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters. (English. Russian original) Zbl 1298.81093

Theor. Math. Phys. 178, No. 1, 76-92 (2014); translation from Teor. Mat. Fiz. 178, No. 1, 88-106 (2014).
Summary: We consider the problem for eigenvalues of a perturbed two-dimensional oscillator in the case of a resonance frequency. The exciting potential is given by a Hartree-type integral operator with a smooth self-action potential. We find asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundary of spectral clusters, which form around energy levels of the nonperturbed operator. To calculate them, we use asymptotic formulas for quantum means.

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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