  By means of the Nyquist method, we investigate the linear stability of
electrostatic waves in homogeneous equilibria of quantum plasmas described by
the Wigner-Poisson system. We show that, unlike the classical Vlasov-Poisson
system, the Wigner-Poisson case does not necessarily possess a Penrose
functional determining its linear stability properties. The Nyquist method is
then applied to a two-stream distribution, for which we obtain an exact,
necessary and sufficient condition for linear stability, as well as to a
bump-in-tail equilibrium.
