Geodesic
Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 894-910.

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The eigenvalue problem for a perturbed two-dimensional resonant oscillator is considered. The exciting potential is given by a nonlocal nonlinearity of Hartree type with smooth self-action potential. To each representation of the rotation algebra corresponds the spectral cluster around an energy level of the unperturbed operator. Asymptotic eigenvalues and asymptotic eigenfunctions close to the lower boundary of spectral clusters are obtained. For their calculation, asymptotic formulas for quantum means are used.
Keywords: self-consistent field, spectral cluster, quantum averaging method, coherent transformation, the WKB approximation, turning point. 
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A. V. Pereskokov. Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 894-910. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a9/

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