Diffusion Processes and Coherent States
S. De Martino, S. De Siena, F. Illuminati, G. Vitiello
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.
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