Perturbation Variation Methods for a Quantum Boltzmann Equation

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