Variational theorems for the single-particle probability density and density matrix in momentum space

Abstract

The existence of Hohenberg-Kohn—like density-functional theorems in momentum space is demonstrated. Invoking principles employed by Levy to construct universal variational density and density-matrix functionals in position space, it is found that (1) there exists a universal variational functional for the one-electron reduced density matrix in momentum space, and (2) for any given external potential, there exists a proper variational functional for the one-electron momentum-space probability density.