Geodesic
Semiclassical asymptotic spectrum of a~Hartree-type operator near the~upper boundary of spectral clusters
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 88-106

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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.
Keywords: self-consistent field, method of quantum averaging, coherent transformation, WKB approximation, spectral cluster, quantum mean. 
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     author = {A. V. Pereskokov},
     title = {Semiclassical asymptotic spectrum of {a~Hartree-type} operator near the~upper boundary of spectral clusters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {88--106},
     publisher = {mathdoc},
     volume = {178},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a2/}
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A. V. Pereskokov. Semiclassical asymptotic spectrum of a~Hartree-type operator near the~upper boundary of spectral clusters. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 88-106. http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a2/