Geodesic
Group-theoretical aspects of the variable frequency oscillator problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 3, pp. 360-374 Cet article a éte moissonné depuis la source Math-Net.Ru

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A group-theoretical intel pretation is given for the variable frequency quantum oscillator in which the frequency dependence on time, $\omega(t)$, is arbitrary. The transition probability, Wren, between states $|n,\omega_{-}\rangle$ and $|m,\omega_{+}\rangle$ with a fixed number of quanta is expressed by means of a matrix element of the $D$-function for the $SU(1,1)$ group. For the case in which frequency varies periodically, the oscillator quasi-energy spectrum is found and its relationship to the properties of the generators of the $SU(1,1)$ group is indicated. It is shown that the problem of spin inversion in an external magnetic field, $\mathbf H(t)$, reduces to solution of the equation of motion for a one-dimensional, variable frequency, classical oscillator. 
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A. M. Perelomov; V. S. Popov. Group-theoretical aspects of the variable frequency oscillator problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 3, pp. 360-374. http://geodesic.mathdoc.fr/item/TMF_1969_1_3_a5/

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