Quantum-Mechanical Modified Boltzmann Equation for Degenerate Internal States

A modified quantum-mechanical Boltzmann equation has been derived for the general case in which the molecules have degenerate internal states. This is an equation of the Boltzmann type for a quantity which is simultaneously a Wigner distribution function in molecular phase space, and a density matrix in internal state space. In particular, the nondiagonal terms of this density matrix have been included in the formalism, resulting in the collision term being modified from the usual Boltzmann expression. Thus the collisions are described in terms of combinations of the Lippmann-Schwinger scattering matrix rather than the collision cross section. For nondegenerate states the usual collision term is obtained again.