Analysis of the Interaction of Matter with Electromagnetic Radiation

Analysis of the interaction of the electromagnetic field and matter is a topical area of research in modern physics. The goal of this paper is to move from mathematical postulates and formalisms of quantum mechanics to equations that include macroscopic variables. In this case, the macroscopic observables are determined by the mean values of the operator corresponding to the observable value, and the mean value is deter-mined by the density matrix. Then the equations are written only through the mean values, by substituting equivalent expressions for the density matrix. As a result, we come to a system of equations expressed in terms of such macroscopic variables as polarization and electromagnetic field. In the semi-classical approach, when the electromagnetic field is not quantized, it is necessary to add the Maxwell's equations of the electromagnetic field to the equations for the mean values. This forms a self-consistent system of equations.