  A set of quantum hydrodynamic equations are derived from the moments of the
electrostatic mean-field Wigner kinetic equation. No assumptions are made on
the particular local equilibrium or on the statistical ensemble wave functions.
Quantum diffraction effects appear explicitly only in the transport equation
for the heat flux triad, which is the third-order moment of the Wigner
pseudo-distribution. The general linear dispersion relation is derived, from
which a quantum modified Bohm-Gross relation is recovered in the long
wave-length limit. Nonlinear, traveling wave solutions are numerically found in
the one-dimensional case. The results shed light on the relation between
quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and
quantum fluid transport around given equilibrium distribution functions.
