Diffusion Processes and Coherent States

Abstract

It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum mechanics, the harmonic-oscillator coherent and squeezed states. The method allows to derive new minimum uncertainty states in time-dependent oscillator potentials and for the Caldirola-Kanai model of quantum damped oscillator.

11 pages, plain LaTeX

Cited by in corpus (4)

• Inference of Planck action constant by a classical fluctuative postulate holding for stable microscopic and macroscopic dynamical systems
• Stochastic Variational Approach to Minimum Uncertainty States
• Extension of Nelson's Stochastic Quantization to Finite Temperature Using Thermo Field Dynamics
• Theory of controlled quantum dynamics