  We study the exact solution for two atomic particles in an optical lattice
interacting via a Feshbach resonance. The analysis includes the influence of
all higher bands, as well as the proper renormalization of molecular energy in
the closed channel. Using an expansion in Bloch waves, we show that the problem
reduces to a simple matrix equation, which can be solved numerically very
efficient. This exact solution allows for the precise determination of the
parameters in the Hubbard model and the two-particle bound state energy. We
identify the regime, where a single band Hubbard model fails to describe the
scattering of the atoms as well as the bound states.
