An alternative derivation of transition amplitudes for time-dependent harmonic oscillators

It is shown that the relations which link the x and p operators of a time-dependent harmonic oscillator to the x and p operators of the corresponding time-independent oscillator can be cast into a generalized Bogoliubov transformation on the standard harmonic oscillator boson creation and annihilation operators. Once this fact has been recognized, various techniques can be invoked to derive in a short way transition amplitudes.