Geodesic
Group-theoretical aspects of the variable frequency oscillator problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 3, pp. 360-374

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_1969_1_3_a5,
     author = {A. M. Perelomov and V. S. Popov},
     title = {Group-theoretical aspects of the variable frequency oscillator problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {360--374},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1969_1_3_a5/}
}
TY  - JOUR
AU  - A. M. Perelomov
AU  - V. S. Popov
TI  - Group-theoretical aspects of the variable frequency oscillator problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1969
SP  - 360
EP  - 374
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1969_1_3_a5/
LA  - ru
ID  - TMF_1969_1_3_a5
ER  - 
%0 Journal Article
%A A. M. Perelomov
%A V. S. Popov
%T Group-theoretical aspects of the variable frequency oscillator problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1969
%P 360-374
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1969_1_3_a5/
%G ru
%F TMF_1969_1_3_a5
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/