Harmonic oscillator with time-dependent mass and frequency and a perturbative potential

Abstract

A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented. The treatment is also applied to the time-dependent oscillator under the action of a time-dependent perturbative potential. The treatment is based on the use of some time-dependent transformations and in the method of invariants of Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)]. Exact coherent states for such systems are also constructed.