Perturbation Variation Methods for a Quantum Boltzmann Equation

Abstract

For molecules with degenerate internal states, the single-particle distribution function must bereplaced by a density matrix, or better, if the translational motion is treated classically, by a Wignerdistribution-function density matrix. The modified BoltzmannIntegro-differential equation for thisquantity has been previously derived but so far only limited solutions of the resulting equation havebeen obtained. Methods are herein discussed which enable the standard methods for the solution ofthe classical Boltzmann equation to be applied to the solution of this equation. Complications involvingcommutation properties are resolved.