Quantum-Mechanical Transport Equation for Atomic Systems

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position $\overrightarrow{\mathrm{R}}$ and moving with classical velocity $\overrightarrow{\mathrm{v}}$ It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The QMTE represents a somewhat different formulation of the problem than that considered in earlier works. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.