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
收藏
页码：532 / 543
页数：12
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