Boltzmann-Vlasov Equation for a Quantum Plasma

Abstract

In this paper a new equation is derived which is a quantum mechanical analog of the classical collisionless Boltzmann equation. To these ends a new quantum mechanical distribution function is employed which is particularly useful in this case. Quantum corrections for longitudinal plasma oscillations are evaluated for a low-density plasma, and it is found that the leading contribution ($\sim {\hslash }^2$) is due to exchange (Pauli principle).