A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, TMF, 2014, Volume 178, Number 1,Pages <nobr>88

This article is cited in 12 papers

Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

A. V. Pereskokov^ab

^a Moscow Power Engineering Institute, Moscow, Russia
^b Moscow Institute for Electronics and Mathematics, Higher School of Economics, Moscow, Russia

Abstract: 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.

Received: 09.06.2013

DOI: 10.4213/tmf8561