Functional N-representability in Density Matrix and Density Functional Theory: An Illustration for Hooke’s Atom

Abstract

A long-standing problem in density matrix theory is that of the N-representability of the reduced p-matrices (or of the reduced p-particle density operators) [1–3]. The cases for p = 1 and p = 2 corresponding to the reduced 1- and 2-matrices, respectively, have been of particular importance in this theory. The latter still lacks a complete solution, although much progress has been accomplished in setting up several N-representability conditions [4–13] and in developing alternative approaches to this problem [14]. The former has been solved for the case of ensembles [1] but still remains unsolved for pure states [15].