Formulas for calculation of transverse dielectric function and transverse electric conductivity in quantum collisional Maxwellian plasma are obtained. The Wigner -Vlasov -Boltzmann kinetic equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate space is used. Various special cases are investigated. Comparison with Lindhard's formula has been carried out.

The analysis of nonlinear interaction of transversal electromagnetic field with Maxwellian collisionless classical and quntum plasmas is carried out. Formulas for calculation electric current in Maxwellian collisionless classical and quntum plasmas are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal current, received at the classical linear analysis. Graphic comparison of density of electric current for classical Maxwellian plasmas and Fermi Dirac plasmas (plasmas with any degree of degeneration of electronic gas) is carried out. Graphic comparison of density of electric current for classical and quantum Maxwellian plasmas is carried out. Also comparison of dependence of density of electric current of quantum Maxwellian plasmas from dimensionless wave number at various values of dimensionless frequency of oscillations of electromagnetic field is carried out.

Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at → 0 the derived formula transfers to the classical one. It is shown also, that when electron collision frequency tends to null (i.e. plasma becomes collisionless), the conductance formula transfers in the known formula inferred earlier by Lindhard.

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Stokes' second problem on the behavior of rarefied gas occupying a half-space is analytically solved. The plane bounding the half-space executes harmonic oscillations. The kinetic equation with the model collision integral in the form of a τ-model is used and the case of diffuse reflection of gas molecules from the wall is considered. The distribution function of gas molecules is constructed and the mass velocity of the gas in the half-space, together with its value directly at the wall, is determined. The drag force acting from the gas on the boundary executing oscillatory motion in its plane is obtained. Moreover, the energy dissipation rate per unit area of the oscillating plate bounding the gas is determined.

We develop a new effective method for solving boundary value problems in kinetic theory. The method permits solving boundary value problems for mirror and diffusive boundary conditions with an arbitrary accuracy and is based on the idea of reducing the original problem to two problems of which one has a diffusion boundary condition for the reflection of molecules from the wall and the other has a mirror boundary condition. We illustrate this method with two classical problems in kinetic theory : the Kramers problem (isothermal slip) and the thermal slip problem. We use the Bhatnagar-Gross-Krook equation (with a constant collision frequency) and the Williams equation (with a collision frequency proportional to the molecular velocity).

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