Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters

被引：4

作者：

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

机构：

[1] Tech Univ, Moscow Power Engn Inst, Moscow, Russia

来源：

IZVESTIYA MATHEMATICS | 2013年 / 77卷 / 01期

关键词：

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

D O I：

10.1070/IM2013v077n01ABEH002632

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the eigenvalue problem for a perturbed two-dimensional oscillator, we suggest a method for constructing asymptotic solutions near the boundaries of spectral clusters by means of a new integral representation and study the issue of calculating the average values of differential operators on the solutions near the boundaries of the clusters.

引用

页码：163 / 210

页数：48

共 40 条

[1] Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
Pereskokov, A. V.
[J]. MATHEMATICAL NOTES, 2012, 92 (3-4) : 532 - 543
[2] Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
A. V. Pereskokov
[J]. Mathematical Notes, 2012, 92 : 532 - 543
[3] Asymptotics of the Spectrum and Quantum Averages of a Hartree Type Operator Near the Lower Boundaries of Spectral Clusters
Vakhrameeva D.A.
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2020, 247 (6) : 820 - 849
[4] Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters
Pereskokov, Alexander
[J]. APPLICABLE ANALYSIS, 2016, 95 (07) : 1560 - 1569
[5] Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Upper Boundaries of Spectral Clusters
Migaeva A.S.
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2020, 251 (6) : 850 - 875
[6] Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Lower Boundaries of Spectral Clusters
Pereskokov A.V.
[J]. Journal of Mathematical Sciences, 2021, 259 (2) : 244 - 263
[7] ASYMPTOTICS OF THE HARTREE OPERATOR SPECTRUM NEAR THE UPPER BOUNDARIES OF SPECTRAL CLUSTERS: ASYMPTOTIC SOLUTIONS LOCALIZED NEAR A CIRCLE
Pereskokov, A. V.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2015, 183 (01) : 516 - 526
[8] Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle
A. V. Pereskokov
[J]. Theoretical and Mathematical Physics, 2015, 183 : 516 - 526
[9] Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
A. S. Migaeva
A. V. Pereskokov
[J]. Mathematical Notes, 2020, 107 : 804 - 819
[10] Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
Migaeva, A. S.
Pereskokov, A. V.
[J]. MATHEMATICAL NOTES, 2020, 107 (5-6) : 804 - 819

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