Formally exact link between electron density and potential energy in single–nondegenerate-band model of an insulating crystal

In a single- , nondegenerate- , band model, the electron density ρ(r) is the sum of the squares of the Wannier function of the band, summed over all lattice sites. X-ray scattering is then determined by the convolution of the momentum eigenfunction of the band, which is the Fourier transform of the Wannier function with itself. Invoking the one-body potential V(r) of density functional theory, a formally exact link is established between ρ(r) and V(r).