  The one-dimensional small-polaron model with open boundary conditions is
considered in the framework of the quantum inverse scattering method. The spin
model which is equivalent to the small-polaron model is the Heisenberg $XXZ$
spin chain in an external magnetic field. For spin model, the solutions of the
reflection equation (RE) and the dual RE are obtained. The eigenvalues and
eigenvectors problems are solved by using the algebraic Bethe ansatz method.
The case of the fermion model is also studied, the commuting of the transfer
matrix can be proved, and the eigenvalues and the Bethe ansatz equations for
fermion model are obtained.
