  The behavior of spin-1/2 particle in a weak static gravitational field is
considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen
transformation providing also the simple form for the momentum and spin
polarization operators. The operator equations of momentum and spin motion are
derived for a first time. Their semiclassical limit is analyzed. The dipole
spin-gravity coupling in the previously found (another) Hamiltonian does not
lead to any observable effects. The general agreement between the quantum and
classical analysis is established, contrary to several recent claims. The
expression for gravitational Stern-Gerlach force is derived. The helicity
evolution in the gravitational field and corresponding accelerated frame
coincides, being the manifestation of the equivalence principle.
