  Based on the analytic model of Feshbach resonances in harmonic traps
described in Phys. Rev. A 83, 030701 (2011) a Bose-Hubbard model is introduced
that provides an accurate description of two atoms in an optical lattice at a
Feshbach resonance with only a small number of Bloch bands. The approach
circumvents the problem that the eigenenergies in the presence of a delta-like
coupling do not converge to the correct energies, if an uncorrelated basis is
used. The predictions of the Bose-Hubbard model are compared to
non-perturbative calculations for both the stationary states and the
time-dependent wavefunction during an acceleration of the lattice potential.
For this purpose, a square-well interaction potential is introduced, which
allows for a realistic description of Feshbach resonances within
non-perturbative single-channel calculations.
