Some model inhomogeneous electron liquid in D dimensions: relation between energy and chemical potential and a spatial generalisation of Kato's nuclear cusp theorem

Abstract

After a brief survey on the application of the Thomas–Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H − as a function of dimensionality D is also briefly referred.