  We present a derivation of the dispersion relation for electrostatic
oscillations (ESOs) in a zero temperature quantum plasma. In the latter,
degenerate electrons are governed by the Wigner equation, while non-degenerate
ions follow the classical fluid equations. The Poisson equation determines the
electrostatic wave potential. We consider parameters ranging from semiconductor
plasmas to metallic plasmas and electron densities of compressed matter such as
in laser-compression schemes and dense astrophysical objects. Due to the wave
diffraction caused by overlapping electron wave function due to the Heisenberg
uncertainty principle in dense plasmas, we have possibility of Landau damping
of the high-frequency electron plasma oscillations (EPOs) at large enough
wavenumbers. The exact dispersion relations for the EPOs are solved numerically
and compared to the ones obtained by using approximate formulas for the
electron susceptibility in the high- and low-frequency cases.
