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 ($\ensuremath{\sim}{\ensuremath{\hbar}}^{2}$) is due to exchange (Pauli principle).
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