The Pauli potential in one-dimensional density functional theory: general result for two-level systems and specific example forNharmonically confined Fermions

Abstract

There is ongoing interest in the kinetic energy functional Ts[ρ] in density functional theory. The present study lies in this area and concerns the Pauli potential VP[ρ]. A differential equation is obtained here for VP(x) in one dimension for a general two-level system. Also, as a specific example, such a functional of ρ(x), the ground-state Fermion density, is given for the case of N Fermions which are harmonically confined.