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Teoreticheskaya i Matematicheskaya Fizika, 1970, Volume 3, Number 3, Pages 377–391 (Mi tmf4121)  

This article is cited in 11 scientific papers (total in 12 papers)

Method of generating functions for a quantum oscillator

A. M. Perelomov, V. S. Popov
References:
Abstract: A method of generating functions is developed for studying a quantum oscillator with a variable frequency $\omega(t)$ subject to the influence of an external force $f(t)$. The method is used to obtain an explicit expression for the transition probabilities $w_{mn}$ between states $|n,\omega_{-}\rangle$ and $|m,\omega_{+}\rangle$, containing a definite number of quanta at the start $(n)$ and end $(m)$ of the process. The Heisenberg representation is discussed and the associated geometrical interpretation of the dynamical variables on the phase plane. By means of the phase plane, formulas are obtained for $w_{mn}$ in the quasiclassical limit (strongly degenerate oscillator for which $m,n\gg 1$). The application of the method of generating functions to the problem of the relaxation of a quantum oscillator interacting with a thermostat is discussed.
Received: 22.09.1969
English version:
Theoretical and Mathematical Physics, 1970, Volume 3, Issue 3, Pages 582–592
DOI: https://doi.org/10.1007/BF01028529
Language: Russian
Citation: A. M. Perelomov, V. S. Popov, “Method of generating functions for a quantum oscillator”, TMF, 3:3 (1970), 377–391; Theoret. and Math. Phys., 3:3 (1970), 582–592
Citation in format AMSBIB
\Bibitem{PerPop70}
\by A.~M.~Perelomov, V.~S.~Popov
\paper Method of generating functions for a~quantum oscillator
\jour TMF
\yr 1970
\vol 3
\issue 3
\pages 377--391
\mathnet{http://mi.mathnet.ru/tmf4121}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 3
\issue 3
\pages 582--592
\crossref{https://doi.org/10.1007/BF01028529}
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  • https://www.mathnet.ru/eng/tmf/v3/i3/p377
  • This publication is cited in the following 12 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
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    Abstract page:792
    Full-text PDF :296
    References:72
    First page:2
     
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