Quantum Mechanical Transport Theory. I. Incoherent Processes

Abstract

The transport of particles through a scattering medium is studied. A generalization of a technique due to Placzek and Wick is used to handle sums over states of excitation of the medium. The collision processes which occur are classified as "inelastic," "elastic," and "quasi-elastic" and correspond to different orderings of the Placzek-Wick series. The inelastic scatterings are described by an essentially classical transport equation and the elastic scatterings by assigning a refractive index to the medium. The "quasi-elastic" scattering involves the excitation of low-lying states of the scattering system. The coherent interference of waves scattered from nearby scatterers is important in this case and depends upon the structure of the medium. In this paper the general theory is developed in terms of a systematic sequence of approximations, of which the first gives just the classical form of transport theory. The correction terms then appear as quantum-mechanical corrections to the classical transport problem.