Theory of self-consistent light-atom interaction

Abstract

The self-consistent set of equations that describes the interaction of an atom with the electromagnetic field is proposed. The set includes the equations for vector and scalar potentials of electromagnetic field vector A(vector r,t), (phi) (vector r,t) and electron current and charge density vector j(vector r,t), (rho) (vector r,t). The obtained equations are similar to the magnetic hydrodynamics equation and differ from them by the presence of the terms depending on the logarithmic gradient of charge density. The specific feature of the obtained equations is that the steady-state distribution of the electron charge and current density is determined by the real and imaginary parts of the Schorodinger equation. The obtained equations are generalized for the relativistic case. In the latter case the equations include the atomic variables of the two types. The atomic variables of the first type are the bilinear forms of the wave function and Dirac conjugated wave function. The atomic variables of second type are the Hermitian conjugated combinations of the wave function first derivative and the Dirac conjugated wave function. Another specific feature of the obtained equations is that the equation for the electron current density can be transformed to the classical Hamilton-Jacobi equation with the new Hamiltonian. The phase of the wave function plays the role of action and new Hamiltonian includes the term depending on the logarithmic gradient of the electron density and its divergence. The relativistic Hamilton-Jacobi equation includes the term depending on the electron spin as well as the terms depending on electron density logarithmic four- gradient and its four-dimensional derivative.