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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 894–910 (Mi mz10621)  

Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator

A. V. Pereskokovab

a National Research University "Moscow Power Engineering Institute"
b National Research University "Higher School of Economics" (HSE), Moscow

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00306
This work was supported by the Russian Science Foundation under grant 14-11-00306.


DOI: https://doi.org/10.4213/mzm10621

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English version:
Mathematical Notes, 2017, 101:6, 1009–1022

Bibliographic databases:

UDC: 517.958+517.928
Received: 17.10.2014
Revised: 30.09.2016

Citation: A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator”, Mat. Zametki, 101:6 (2017), 894–910; Math. Notes, 101:6 (2017), 1009–1022

Citation in format AMSBIB
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