Boundary Problems for a Quantum Fermi Gas

We derive a relaxation kinetic equation describing the behavior of Fermi gases. We consider the Kramers problem for the isothermal slipping in a half-space and obtain an analytic solution of the problem and the explicit form of the distribution function for particles moving toward the wall. We analyze the dependence of the equation itself and the slipping velocity on the parameter, the ratio between the chemical potential and the product of the Boltzmann constant and the absolute temperature.