Periodic potentials are of fundamental importance to many interesting experimental and

theoretical systems. Although the eigenstates of an ideal periodic potential are perfectly

delocalized, perhaps of greater interest are so-called Wannier functions, which represent

maximally localized electronic states in a crystal. In higher dimensions with complicated

potentials, such states are dicult to calculate analytically and are instead often found

via numerical optimization algorithms. However, these methods compromise the physical

reliability and intuition of the resulting outputs. We implement and generalize an analytic

method to calculate maximally localizedWannier functions that is designed for optical lattice

experiments. With this method, full Bose-Hubbard parameters can be calculated from the

input of a fairly general lattice beam conguration. This will be useful for the eventual

realization of such systems via optical lattice experiments.