  It is shown that the exact Foldy-Wouthuysen transformation for spin-0
particles on spacetimes described by the metrics $ds^2 = V^2 dt^2 - W^2 d
{\bf{x}}^2$, where $V=V({\bf{x}})$ and $W=W({\bf{x}})$, only exists if the
scalar field is nonminimally coupled to the Ricci scalar field with a coupling
constant equal to 1/6. The nonminimal coupling term, in turn, does not violate
the equivalence principle. As an application we obtain the nonrelativistic
Foldy-Wouthuysen Hamiltonian concerning the general solution to the linearized
field equations of higher-derivative gravity for a static pointlike source in
the Teyssandier gauge.
