Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 201, Number 3, Pages 382–414
DOI: https://doi.org/10.4213/tmf9639 (Mi tmf9639) 		 
This article is cited in 32 scientific papers (total in 32 papers)

Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems

A. Yu. Anikinab, S. Yu. Dobrokhotovab, V. E. Nazaikinskiiab, A. V. Tsvetkovaab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia
Full-text PDF (908 kB) Citations (32)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf9639
Abstract: We consider stationary scalar and vector problems for differential and pseudodifferential operators leading to the appearance of asymptotic solutions of one-dimensional problems localized in a neighborhood of intervals (“bound states”). Based on the semiclassical approximation and the Maslov canonical operator, we develop a constructive algorithm that allows writing an asymptotic solution globally under certain conditions using an Airy function of complex argument.
Keywords: semiclassical asymptotic solution, bound state, closed trajectory, WKB approximation, canonical operator, Airy function.
Funding agency Grant number
Russian Science Foundation 16-11-10282
This research is supported by a grant from the Russian Science Foundation (Project No. 16-11-10282).
Received: 09.10.2018
Revised: 03.09.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 201, Issue 3, Pages 1742–1770
DOI: https://doi.org/10.1134/S0040577919120079
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems”, TMF, 201:3 (2019), 382–414; Theoret. and Math. Phys., 201:3 (2019), 1742–1770
Citation in format AMSBIB
\Bibitem{AniDobNaz19}
\by A.~Yu.~Anikin, S.~Yu.~Dobrokhotov, V.~E.~Nazaikinskii, A.~V.~Tsvetkova
\paper Uniform asymptotic solution in the~form of an~Airy function for semiclassical bound states in one-dimensional and radially symmetric problems
\jour TMF
\yr 2019
\vol 201
\issue 3
\pages 382--414
\mathnet{http://mi.mathnet.ru/tmf9639}
\crossref{https://doi.org/10.4213/tmf9639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4036829}
\elib{https://elibrary.ru/item.asp?id=43225797}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 3
\pages 1742--1770
\crossref{https://doi.org/10.1134/S0040577919120079}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000511860000007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077625245}
Linking options:
  • https://www.mathnet.ru/eng/tmf9639
  • https://doi.org/10.4213/tmf9639
  • https://www.mathnet.ru/eng/tmf/v201/i3/p382
    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:633
    Full-text PDF :153
    References:75
    First page:13
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024