  Quantum mechanical averaging of the particle concentration operator is an
effective starting point for derivation of the many-particle quantum
hydrodynamic equations. In many-particle quantum systems, we have to separate
the ordered motion of the local center of mass (velocity field), the thermal,
and the quantum motion. The quantum mechanical average process, invoked here,
is completely determined, and is different from the usual averaging processes
that introduces undefined probabilities for quantum states. It is shown that
the Madelung decomposition for the $N$-particle spinor wave function allows the
correct introduction of the velocity field, and gives explicit expressions for
the quantum contributions to both the momentum, and the spin flux. The
formalism also contains plasma effects produced by the Coulomb and spin-spin
interparticle interactions. It is shown that both interactions appear in plasma
dynamics as effective electric and magnetic fields. As result we find a fully
coherent description for spin quantum plasma in the self-consistent field
approximation for interparticle interactions. A simple consequence - the change
brought about by interparticle correlations on the propagation of electrostatic
waves in a spin quantum plasma - is discussed.
