Loading [MathJax]/jax/output/SVG/config.js
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, 2022, Volume 211, Number 3, Pages 455–468
DOI: https://doi.org/10.4213/tmf10281 (Mi tmf10281) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation

Yu. A. Grishechkin, V. N. Kapshai

Francisk Skorina Gomel State University, Gomel, Belarus
Full-text PDF (541 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf10281
Abstract: We construct approximate analytic solutions of the Logunov–Tavkhelidze equation in the case of a potential that, in the one-dimensional relativistic configuration representation, has the form analogous to the potential of the nonrelativistic harmonic oscillator in the coordinate representation. The wave functions are obtained in both the momentum and relativistic configuration representations. The approximate values of the energy of the relativistic harmonic oscillator are the roots of transcendental equations. The wave functions in the relativistic configuration representation have additional zeros in comparison with the wave functions of the corresponding states of the nonrelativistic harmonic oscillator in the coordinate representation.
Keywords: quasipotential equation, relativistic configuration representation, integral equation, harmonic oscillator, wave function, energy spectrum, Sturm–Liouville problem, Macdonald function.
Received: 07.03.2022
Revised: 19.03.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 211, Issue 3, Pages 826–837
DOI: https://doi.org/10.1134/S0040577922060058
Bibliographic databases:
Document Type: Article
PACS: 02.30.Gp, 02.30.Hq, 03.65.-w, 03.65.Ge
MSC: 33B15, 33C20, 34B24, 34B30, 34B40, 45B05
Language: Russian
Citation: Yu. A. Grishechkin, V. N. Kapshai, “Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation”, TMF, 211:3 (2022), 455–468; Theoret. and Math. Phys., 211:3 (2022), 826–837
Citation in format AMSBIB
\Bibitem{GriKap22}
\by Yu.~A.~Grishechkin, V.~N.~Kapshai
\paper Approximate analytic solution of the~Logunov--Tavkhelidze equation for a~one-dimensional oscillator potential in the~ relativistic configuration representation
\jour TMF
\yr 2022
\vol 211
\issue 3
\pages 455--468
\mathnet{http://mi.mathnet.ru/tmf10281}
\crossref{https://doi.org/10.4213/tmf10281}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461536}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...211..826G}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 211
\issue 3
\pages 826--837
\crossref{https://doi.org/10.1134/S0040577922060058}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140901310}
Linking options:
  • https://www.mathnet.ru/eng/tmf10281
  • https://doi.org/10.4213/tmf10281
  • https://www.mathnet.ru/eng/tmf/v211/i3/p455
    • This publication is cited in the following 1 articles:
    1. Sh. M. Nagiyev, R. M. Mir-Kasimov, “Relativistic linear oscillator under the action of a constant external force. Transition amplitudes and the Green's function”, Theoret. and Math. Phys., 214:1 (2023), 72–88  mathnet  crossref  crossref  mathscinet  adsnasa
    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:368
    Full-text PDF :38
    References:81
    First page:18
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025