I'm interested in calculating scattering processes (e.g. Coulomb scattering of an electron beam by a single ion) in the context of lattice quantum field theory, and wonder if there is something like the expansion of a plane wave in spherical harmonics on the lattice? (I mean in discrete space modeled by a three dimensional, finite, cubic lattice.)
So I am looking for an orthonormal basis for complex valued functions on a finite lattice, where the angular and radial variables would be (approximately?) separated, as this is the case for the solid harmonics.
Thank you for your help!