• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Book chapter
  • Квазиклассическая асимптотика собственных функций возмущенного осциллятора вблизи верхних границ спектральных кластеров
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 17, 2026
'I Wish That People Would Place Greater Trust in Science'
When Tatiana Eremicheva chose Fundamental and Computational Linguistics as her field of study, she thought it would be about learning languages. Instead, she discovered it was about helping people. In this interview for the HSE Young Scientists project, she discusses science as a way of understanding the world, billiards as a team-building activity, and why learning to read is not always as easy as it seems.
September 15, 2026
Immunity to Chaos: How Personal Resources Help Us Cope with the Challenges of a Turbulent World
International conflicts, crises and digital overload—the modern world puts our minds to the test every day. Traditional psychology often focuses on the consequences: anxiety, depression, and psychosomatic disorders. But what if we looked at the problem differently—through the lens of the resources that prevent us from breaking down? Psychological immunity is precisely this set of resources. Alena Zolotareva and her group, Psychological Immunity as a Resource for Positive Functioning, are developing an integrative model of this phenomenon, adapting diagnostic tools and preparing for large-scale empirical research. Why do psychologists need to collaborate with medical professionals, and how could their research transform preventive care in clinics and corporations?
September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Квазиклассическая асимптотика собственных функций возмущенного осциллятора вблизи верхних границ спектральных кластеров

С. 237–239.
А.В. Перескоков
Language: Russian
Full text
Keywords: Асимптотическое разложениеasymptotic solutioncoherent transformationкогерентное преобразованиевозмущенный осцилляторperturbed oscillator

In book

Воронежская зимняя матаматическая школа С. Г. Крейна - 2026.
Воронеж: Издательский дом ВГУ, 2026.
Similar publications
Нахождение формальных степенно–логарифмических разложений решений 𝑞–разностных уравнений
Gaianov N., Parusnikova A., Уфимский математический журнал 2026 Т. 18 № 2 С. 14–22
We consider an algebraic 𝑞–difference equation. We propose a sufficient condition for the existence of a formal power–logarithmic expansion in the vicinity of zero of the solution to such an equation. We apply this sufficient condition to construct the formal expansion of a solution to a certain 𝑞–difference analogue of the fifth Painlevé equation for particular ...
Added: June 24, 2026
Asymptotic expansion of self-consistent energy levels of hydrogen atom in ortogonal electric and magnetic fields
A. V. Pereskokov, Theoretical and Mathematical Physics 2026 Vol. 226 No. 3 P. 470–484
We consider the spectral problem for a hydrogen atom in orthogonal electric and magnetic fields with an additional self-consistent field. We obtain an asymptotic expansion of self-consistent energy levels. We find an asymptotic expansion of asymptotic eigenfunctions near the sphere |q| = 2. We calculate the asymptotics of their norm in the space L2(R3). ...
Added: April 12, 2026
Asymptotics of eigenfunctions of perturbed resonance oscillator near upper boundaries of spectral clusters
A. V. Pereskokov, Journal of Mathematical Sciences 2025 Vol. 291 No. 4 P. 544–553
We study the eigenvalue problem for a perturbed resonance oscillator. We find asymptotic expansions of coherent states of the algebra su(2). We show that the asymptotic eigenfunctions are localized near a circle and construct an expansion of asymptotic eigenfunctions near this circle. ...
Added: December 7, 2025
Квазиклассическая асимптотика самосогласованных уровней энергии
А.В. Перескоков, В кн.: Современные методы теории краевых задач. Понтрягинские чтения — XXXVI : материалы международной конференции: Воронежская весенняя математическая школа посвященная памяти С. М. Никольского ( 30 апреля - 4 мая 2025 г.).: Издательский дом ВГУ, 2025. С. 249–250.
Найдена серия асимптотических собственных значений для атома водорода в магнитном поле, возмущенном самосогласованным полем. ...
Added: June 16, 2025
Об асимптотике самосогласованных уровней энергии
Перескоков А.В., В кн.: Сборник тезисов международной конференции "Дифференциальные уравнения и смежные вопросы", 25-е совместное заседание Московского математического общества и Семинара имени И.Г.Петровского Москва, 19– 24 мая 2025.: MSU Pub, 2025. С. 236–238.
Рассмотрена спектральная задача   для атома водорода в магнитном поле, возмущенном самосогласованным полем. Получено асимптотическое   разложение самосогласованных уровней энергии. ...
Added: June 15, 2025
Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels
A. V. Pereskokov, Theoretical and Mathematical Physics 2025 Vol. 222 No. 3 P. 453–470
The spectral problem for the hydrogen atom in a magnetic field perturbed by a self-consistent field is considered. An asymptotic expansion of self-consistent energy levels is obtained. An asymptotic expansion of hypergeometric coherent states near the sphere |q| = 2 is found. The asymptotics of the norm of the asymptotic eigenfunctions in the space L2(R3) is calculated. ...
Added: April 24, 2025
Integral Representation and Asymptotic Expansion for Hypergeometric Coherent States
Pereskokov A., Mathematics 2022 Vol. 10 No. 16 Article 2907
An integral representation is found for hypergeometric coherent states. It contains a generalized hypergeometric function. An asymptotic expansion of hypergeometric coherent states near (Formula presented.) is constructed. This expansion is used to find asymptotic eigenfunctions of the Hamiltonian of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters. © 2022 ...
Added: October 24, 2022
Asymptotic Expansions of Solutions to the Second Term of the Fourth Painlevé Hierarchy
Anoshin V. I., Beketova A., Parusnikova A. et al., Programming and Computer Software 2022 Vol. 48 No. 1 P. 30–35
Asymptotic behavior and asymptotic expansions of solutions to the second term of the fourth Painlevé hierarchy are constructed using power geometry methods [1]. Only results for the case of general position—for the equation parameters β,δ≠0β,δ≠0—are provided. For constructing asymptotic expansions, a code written in a computer algebra system is used. ...
Added: February 5, 2022
Semiclassical asymptotics of the spectrum of the hydrogen atom in an electromagnetic field near the lower boundaries of spectral clusters
Pereskokov A., Journal of Mathematical Sciences 2021 Vol. 259 No. 2 P. 244–263
We study the Zeeman–Stark effect problem in the hydrogen atom located in an electromagnetic field by using irreducible representations of the Karasev–Novikova algebra with quadratic commutation relations. We find asymptotics of a series of eigenvalues and the corresponding eigenfunctions near the lower boundaries of spectral clusters. ...
Added: December 6, 2021
ASYMPTOTICS OF THE FILTRATION PROBLEM WITH ALMOST CONSTANT COEFFICIENTS
LIUDMILA I. KUZMINA, OSIPOV Y., International Journal for Computational Civil and Structural Engineering 2021 Vol. 17 No. 2 P. 43–49
During the construction of hydraulic and underground structures, a grout solution is pumped into the ground to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through the pores of ...
Added: October 18, 2021
Asymptotics of inverse filtration problem in porous media
Liudmila Kuzmina, Osipov Y. V., Tzariova V., , in: IOP Conference Series: Materials Science and Engineering 1030 (2021) VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, UzbekistanVol. 1030: VII International Scientific Conference "Integration, Partnership and Innovation in Construction Science and Education" (IPICSE 2020) 11th-14th November 2020, Tashkent, Uzbekistan.: IOP Publishing, 2021. Ch. 012109 P. 1–7.
Filtration problems arise in the design of tunnels and underground structures. A onedimensional filtration model of a monodisperse suspension in a homogeneous porous medium is considered. For a general nonlinear filtration function, an asymptotic solution is constructed behind the concentrations front of suspended and retained particles. It is shown that the asymptotics is close to the numerical solution. Comparison ...
Added: July 3, 2021
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., Journal of Mathematical Sciences 2020 Vol. 251 No. 6 P. 850–875
We study the Zeeman-Stark effect in the hydrogen atom located in an electromagnetic field by using irreducible representations of an algebra with the Karasev-Novikova quadratic commutation relations. The representations are associated with resonance spectral clusters near the energy level of the unperturbed hydrogen atom. We find asymptotics for a series of eigenvalues and corresponding asymptotic eigenfunctions near the ...
Added: December 7, 2020
Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters
Migaeva A. S., A. V. Pereskokov, Mathematical notes 2020 Vol. 107 No. 5 P. 804–819
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. ...
Added: June 30, 2020
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, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 391–400
The problem of the Zeemann–Stark effect for the hydrogen atom in electromagnetic fields is considered using the irreducible representations of the Karasev–Novikova algebra with quadratic commutation relations. An asymptotics of the series of eigenvalues and the asymptotic eigenfunctions are obtained near the upper boundaries of resonance spectral clusters which are formed near the energy levels of an unperturbed hydrogen ...
Added: November 16, 2019
Global asymptotics of filtration in porous media
Liudmila Kuzmina, Osipov Y., Zheglova Y., , in: E3S Web of Conferences Volume 97 (2019) XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019)Vol. 97: XXII International Scientific Conference “Construction the Formation of Living Environment” (FORM-2019).: EDP Sciences, 2019. Ch. 05002 P. 1–8.
Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The ...
Added: July 7, 2019
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit