Kinetic Equation for Plasma

The collision integral for the kinetic equation describing a qunatum mechanical plasma is set up. It is shown that the classical collision integral derived by Rostoker, Rosenbluth, Balescu, and Lenard is easily obtained from the more perspicuous quantum mechanical result by letting $\hslash \to 0$. The kinetic equations of Pines and Schrieffer, which describe the interactions of the electrons with plasma oscillations, are obtained by isolating the contributions from the plasma oscillations.