  We carry out a systematic study of the dispersion relation for linear
electrostatic waves in an arbitrarily degenerate quantum electron plasma. We
solve for the complex frequency spectrum for arbitrary values of wavenumber $k$
and level of degeneracy $\mu$. Our finding is that for large $k$ and high $\mu$
the real part of the frequency $\omega_{r}$ grows linearly with $k$ and scales
with $\mu$ only because of the scaling of the Fermi energy. In this regime the
relative Landau damping rate $\gamma/\omega_{r}$ becomes independent of $k$ and
varies inversly with $\mu$. Thus, damping is weak but finite at moderate levels
of degeneracy for short wavelengths.
