  A dispersion equation, which describes the interaction of low density
electron beam with a degenerate electron quantum plasma, is derived and
examined for some interesting cases. In addition to the instabilities similar
to those for classical plasma, due to the quantum effect a new type of
instability is found. Growth rates of these new modes, which are purely
quantum, are obtained. Furthermore, the excitation of Bogolyubov's type of
spectrum by a strong electric field is discussed.
