  We give an example of a mathematical model describing quantum mechanical
processes interacting with medium. As a model, we consider the process of heat
scattering of a wave function defined on the phase space. We consider the case
when the heat diffusion takes place only with respect to momenta. We state and
study the corresponding modified Kramers equation for this process. We consider
the consequent approximations to this equation in powers of the quantity
inverse to the medium resistance per unit of mass of the particle in the
process. The approximations are constructed similarly to statistical physics,
where from the usual Kramers equation for the evolution of probability density
of the Brownian motion of a particle in the phase space, one deduces an
approximate description of this process by the Fokker--Planck equation for the
density of probability distribution in the configuration space. We prove that
the zero (invertible) approximation to our model with respect to the large
parameter of the medium resistance, yields the usual quantum mechanical
description by the Schr\"odinger equation with the standard Hamilton operator.
We deduce the next approximation to the model with respect to the negative
power of the medium resistance coefficient. As a result we obtain the modified
Schr\"odinger equation taking into account dissipation of the process in the
initial model.
