Fourier expansions for the potentials of lattices of charge

Abstract

We apply the Poisson sum rule to obtain formal expressions for the Fourier coefficients of the potential of a lattice of generalized charge. Each generalized charge is assumed to contribute to the potential a term which depends only on the vector displacement from the charge's location. The coefficients are explicitly calculated for Coulomb and Yukawa-type individual particle potentials. The potentials of finite and disordered lattices are also briefly considered.