Some New Aspects of Degenerate Quantum Plasma
  Answers to some salient questions, which arise in quantum plasmas, are given.
Starting from the Schr\"{o}dinger equation for a single particle it is
demonstrated how the Wigner-Moyal equation can be derived. It is shown that the
Wigner-Moyal type of equation also exists in the classical field theory. As an
example, from the Maxwell equations the Wigner-Moyal type of equation is
obtained for a dense photon gas, which is classical, concluding that the
Wigner-Moyal type of equation can be derived for any system, classical or
quantum. A new type of quantum kinetic equations are presented. These novel
kinetic equations allow to obtain a set of quantum hydrodynamic equations,
which is impossible to derive by the Wigner-Moyal equation. The propagation of
small perturbations and instabilities of these perturbations are then
discussed, presenting new modes of quantum plasma waves. In the case of low
frequency oscillations with ions, a new Bogolyubov type of spectrum is found.
Furthermore, the Korteweg-de Vries (KdV) equation is derived and the
contribution of the Madelung term in the formation of the KdV solitons is
discussed.
