  We describe quantum hydrodynamic equations with the Coulomb exchange
interaction for three and two dimensional plasmas. Explicit form of the force
densities are derived. We present non-linear Schrodinger equations (NLSEs) for
the Coulomb quantum plasmas with the exchange interaction. We show contribution
of the exchange interaction in the dispersion of the Langmuir, and ion-acoustic
waves. We consider influence of the spin polarization ratio on strength of the
Coulomb exchange interaction. This is important since exchange interaction
between particles with same spin direction and particles with opposite spin
directions are different. At small particle concentrations
$n_{0}<<10^{25}cm^{-3}$ and small polarization the exchange interaction gives
small decrease of the Fermi pressure. With increasing of polarization role of
the exchange interaction becomes more important, so that it can overcome the
Fermi pressure. The exchange interaction also decreases contribution of the
Langmuir frequency. Ion-acoustic waves do not exist in limit of large
polarization since the exchange interaction changes the sign of pressure. At
large particle concentrations $n_{0}>>10^{25}cm^{-3}$ the Fermi pressure
prevails over the exchange interaction for all polarizations. Similar picture
we obtain for two dimensional quantum plasmas.
