Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters

被引：0

作者：

Migaeva, A. S. ^{[1
]}

Pereskokov, A. V. ^{[1
,2
]}

机构：

[1] Natl Res Univ, Moscow Power Engn Inst, Moscow 111250, Russia

[2] Natl Res Univ Higher Sch Econ, Moscow 101000, Russia

来源：

MATHEMATICAL NOTES | 2020年 / 107卷 / 5-6期

基金：

俄罗斯科学基金会;

关键词：

spectral cluster; quantum averaging method; WKB-approximation; coherent transformation;

D O I：

10.1134/S0001434620050089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Zeeman-Stark effect for the hydrogen atom in an electromagnetic field is considered by using irreducible representations of an algebra with Karasev-Novikova quadratic commutation relations. The asymptotics of the series of eigenvalues and asymptotic eigenfunctions are obtained near the lower boundaries of the resonance spectral clusters, which are formed near the energy levels of the unperturbed hydrogen atom.

引用

页码：804 / 819

页数：16

共 50 条

[1] 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
[2] On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters
A. V. Pereskokov
[J]. Russian Journal of Mathematical Physics, 2019, 26 : 391 - 400
[3] On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters
Pereskokov, A. V.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2019, 26 (03) : 391 - 400
[4] 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
[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] Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters
Pereskokov, Alexander
[J]. APPLICABLE ANALYSIS, 2016, 95 (07) : 1560 - 1569
[7] 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
[8] Asymptotics of Spectral Clusters for a Perturbation of the Hydrogen Atom
Alejandro Uribe
Carlos Villegas-Blas
[J]. Communications in Mathematical Physics, 2008, 280 : 123 - 144
[9] Asymptotics of spectral clusters for a perturbation of the hydrogen atom
Uribe, Alejandro
Villegas-Blas, Carlos
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 280 (01) : 123 - 144
[10] Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters
Pereskokov, A. V.
[J]. IZVESTIYA MATHEMATICS, 2013, 77 (01) : 163 - 210

← 1 2 3 4 5 →