  In this paper, we obtain a nonrelativistic Hamiltonian from the
Lorentz-violating (LV) scalar Lagrangian in the minimal SME. The Hamiltonian is
obtained by two different methods. One is through the usual ansatz
$\Phi(t,\vec{r})=e^{-imt}\Psi(t,\vec{r})$ applied to the LV corrected
Klein-Gordon equation, and the other is the Foldy-Wouthuysen transformation.
The consistency of our results is also partially supported by the comparison
with the spin-independent part of the fermion Hamiltonian. In this comparison,
we can also establish a relation between the set of scalar LV coefficients with
their fermion counterparts. Using a pedagogical definition of the weak
equivalence principle (WEP), we further point out that the LV Hamiltonian not
only necessarily violates universal free fall, which is clearly demonstrated in
the geodesic deviation, but also violates WEP in a semi-classical setting. As a
bosonic complement, this method can be straightforwardly applicable to the
spin-1 case, which shall be useful in the analysis of atomic tests of WEP, such
as the case of the $^{87}\text{Rb}_1$ atom.
