Unitary relations in time-dependent harmonic oscillators

Abstract

For a harmonic oscillator with time-dependent (positive) mass and frequency, an 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 frequency, as well as operators. For a driven harmonic oscillator, an unitary transformation which relates the driven system and the system of same mass and frequency without driving force is given, as a generalization of previous results, in terms of the solution of classical equation of motion of the driven system. These transformations, thus, give a simple way of finding exact wave functions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.