  The Kerr metric of spherically symmetric gravitational field is analyzed
through the coordinate transformation from the rotating frame to fixing frame,
and consequently that the inertial force field (with the exception of the
centrifugal force field) in the rotating system is one part of its
gravitomagnetic field is verified. We investigate the spin-rotation coupling
and, by making use of Lewis-Riesenfeld invariant theory, we obtain exact
solutions of the Schr\"{o}dinger equation of a spinning particle in a
time-dependent rotating reference frame. A potential application of these exact
solutions to the investigation of Earth$^{,}$s rotating frequency fluctuation
by means of neutron-gravity interferometry experiment is briefly discussed in
the present paper.
