Resolutions of the Coulomb operator

Abstract

We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1∕r₁₂ and propose that the resulting “resolution of the Coulomb operator,” r₁₂⁻¹=∣ϕi><ϕi∣, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges. Show more