LANGEVIN QUANTIZATION OF THE TIME-DEPENDENT HARMONIC-OSCILLATOR

As an application of the recently proposed Langevin formulation of qua ntum dynamics, we quantize the time-dependent harmonic oscillator. In this way, we are able to explicitly compute the quantum-mechanical pro pagator. At variance with previous results, the expression found in th is letter contains no auxiliary function to be determined by solving ( as yet unsolved) non-linear differential equations, but it is written in terms of two series which arise quite naturally within the present formalism. Our strategy is compared with ordinary time-dependent pertu rbation theory.