Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators

被引：4

作者：

Pereskokov, A. V. ^{[1
]}

机构：

[1] Moscow Inst Power Engn, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 92卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

spectral cluster; resonance; operator averaging method; coherent transform; WKB-approximation; turning point; POLYNOMIAL COMMUTATION RELATIONS; ALGEBRA;

D O I：

10.1134/S0001434612090258

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The eigenvalue problem for the perturbed resonant oscillator is considered. A method for constructing asymptotic solutions near the boundaries of spectral clusters using a new integral representation is proposed. The problem of calculating the averaged values of differential operators on solutions near the cluster boundaries is studied.

引用

页码：532 / 543

页数：12

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[1] Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
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[2] Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters
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