Geodesic
Method of generating functions for a quantum oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 3, pp. 377-391 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Method of generating functions for a~quantum oscillator},
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A. M. Perelomov; V. S. Popov. Method of generating functions for a quantum oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 3, pp. 377-391. http://geodesic.mathdoc.fr/item/TMF_1970_3_3_a7/

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