  A structure of generator of a quantum dynamical semigroup for the dynamics of
a test particle interacting through collisions with the environment is
considered, which has been obtained from a microphysical model. The related
master-equation is shown to go over to a Fokker-Planck equation for the
description of Brownian motion at quantum level in the long wavelength limit.
The structure of this Fokker-Planck equation is expressed in this paper in
terms of superoperators, giving explicit expressions for the coefficient of
diffusion in momentum in correspondence with two cases of interest for the
interaction potential. This Fokker-Planck equation gives an example of a
physically motivated generator of quantum dynamical semigroup, which serves as
a starting point for the theory of measurement continuous in time, allowing for
the introduction of trajectories in quantum mechanics. This theory had in fact
already been applied to the problem of Brownian motion referring to similar
phenomenological structures obtained only on the basis of mathematical
requirements.
