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Teoreticheskaya i Matematicheskaya Fizika, 1970, Volume 3, Number 3, Pages 377–391
(Mi tmf4121)
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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
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
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
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https://www.mathnet.ru/eng/tmf4121 https://www.mathnet.ru/eng/tmf/v3/i3/p377
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Abstract page: | 792 | Full-text PDF : | 294 | References: | 69 | First page: | 2 |
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