Langevin Quantization of the Time-Dependent Harmonic Oscillator
Antonio Defendi, Marco Roncadelli · Europhysics Letters (EPL) · 1993
As an application of the recently proposed Langevin formulation of quantum dynamics, we quantize the time-dependent harmonic oscillator. In this way, we are able to explicitly compute the quantum-mechanical propagator. At variance with previous results, the expression found in this 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 perturbation theory.