Unitary relations in time-dependent harmonic oscillators

For a harmonic oscillator with time-dependent (positive) mass and frequency , a unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent f requency, as well as operators. For a driven harmonic oscillator, a unitary transformation which relates the driven system and a system of the same ma ss and frequency without a driving force is given, as a generalization of p revious results, in terms of the solution of classical equation of motion o f the driven system. Thus transformations give a simple way of finding exac t wavefunctions of a driven harmonic oscillator system, provided the quantu m states of the corresponding system of unit mass are given.