  We propose an easy to use model to solve for interacting atoms in an optical
lattice. This model allows for the whole range of weakly to strongly
interacting atoms, and it includes the coupling between relative and
center-of-mass motion via anharmonic lattice terms. We apply this model to a
high-precision spin dynamics experiment, and we discuss the corrections due to
atomic interactions and the anharmonic coupling. Under suitable experimental
conditions, energy can be transferred between the relative and center-of-mass
motion, and this allows for creation of Feshbach molecules in excited lattice
bands.
