Quantum-Mechanical Boltzmann Equation

A Boltzmann equation is derived from the N-particle Schrödinger equation. The development is based on the solution of the two-particle quantum-mechanical Liouville equation due to Green. The various approximations involved in the derivation are discussed and the collision integral and corrections are compared to their classical analogs. Further development of the collision integral yields the standard result, the usual Boltzmann collision integral in which the classical differential cross section is replaced by its quantum-mechanical counterpart.