  The kinetic equation of Wigner -- Vlasov -- Boltzmann with collision integral
in relaxation BGK (Bhatnagar, Gross and Krook) form in coordinate space for
quantum non--degenerate (Maxwellian) collisional plasma is used. Exact
expression (within the limits of considered model) is found. The analysis of
longitudinal dielectric permeability is done. It is shown that in the limit
when Planck's constant tends to zero of expression for dielectric permettivity
transforms into the classical case of dielectric permettivity. At small values
of wave number it has been received the solution of the dispersion equation.
Damping of plasma oscillations has been analized. The analytical comparison
with the dielectric Mermin' function received with the use of the kinetic
equation in momentum space is done. Graphic comparison of the real and
imaginary parts of dielectric permettivity of quantum and classical plasma is
done also.
