GENERALIZED LANGEVIN QUANTIZATION

The recently proposed Langevin formulation of quantum dynamics yields the quantum mechanical propagator at imaginary time as a noise average which involves the solutions of a Langevin equation in configuration space with a Gaussian white noise. This strategy does not require any knowledge about the ground-state quantum dynamics and has been success ful in dealing with certain as yet unsolved problems. Here we sketch a generalization of this approach which is based on a similar Langevin equation, whose drift however contains an arbitrary function. As it tu rns out, this freedom leads to a great simplification in the treatment of several quantum mechanical systems as compared to the original Lan gevin formulation (this point is illustrated by taking the forced harm onic oscillator as an example). We also show that when the above-menti oned arbitrary function obeys the imaginary-time Hamilton-Jacobi equat ion, then the new formulation of quantum dynamics exhibits a manifest connection with classical mechanics (at imaginary time).