The Statistical-Mechanical Theory of Transport Processes. VIII. Quantum Theory of Transport in Gases

Abstract

The quantum-mechanical analog of the Maxwell-Boltzmann equation of transport in gases of low density is derived from the quantum-mechanical equation for the motion in phase space of the Wigner function. The derivation is based upon the theory of phase-space transformation functions which is developed in this article. Although the present treatment resembles the derivation of Mori and Ono, it is simpler and more general. Particularly, the assumption of random a priori phases, an integral part of Mori and Ono's work, need not be applied explicitly. The Uhling and Uhlenbeck equation is verified in the Born collision approximation.