  We study the interaction of a scalar and a spinning particle with a coherent
linearized gravitational wave field treated as a classical spin two external
field. The spin degrees of freedom of the spinning particle are described by
skew-commuting variables. We derive the explicit expressions for the
eigenfunctions and the Green's functions of the theory. The discussion is exact
within the approximation of neglecting radiative corrections and we prove that
the result is completely determined by the semiclassical contribution.
