  A consideration of waves propagating parallel to the external magnetic field
is presented. The dielectric permeability tensor is derived from quantum
kinetic equations with non-trivial equilibrium spin-distribution functions
(NTESDF) in the linear approximation on amplitude of wave perturbations. In
general case, x- and y-projections of the SDF are nonzero which is called the
non-trivial regime. Corresponding equilibrium solution is found. Contribution
of the NTESDF appears in the dielectric permeability tensor in the additive
form. It is explicitly found here. Corresponding modification in the dispersion
equation for the transverse waves is derived. Contribution of NTESDF in the
spectrum of transverse waves is calculated numerically. It is found that the
term caused by the NTESDF can be comparable with the classic terms for the
relatively small wave vectors and frequencies above the cyclotron frequency. In
majority of regimes, the extra spin caused term dominates over the spin term
found earlier, except the small frequency regime, where their contributions in
the whistler spectrum are comparable. A decrease of the left-hand circularly
polarized wave frequency, an increase of the high-frequency right-hand
circularly polarized wave frequency, and a decrease of frequency changing by an
increase of frequency at the growth of the wave vector for the whistler are
found. A dramatic decrease of the spin wave frequency resulting in several
times larger group velocity of the spin wave is found either. Found dispersion
equations are used for obtaining of an effective quantum hydrodynamics
reproducing these results. This generalization requires the introduction of
corresponding equation of state for the thermal part of the spin current in the
spin evolution equation.
