Hohenberg-Kohn and Percus-Levy-Lieb proofs of density-functional theory

Authors

Viraht Sahni, CUNY Graduate Center and CUNY Brooklyn CollegeFollow
Xiao-Yin Pan, Ningbo University

Document Type

Article

Publication Date

5-2-2012

Abstract

The premise of density-functional theory is that knowledge of the ground-state density uniquely determines the Hamiltonian, and thereby, via solution of the corresponding time-independent Schrodinger equation, all the properties of the system. The density therefore constitutes a basic variable of quantum mechanics. There are at present two paths from the density to the Hamiltonian: the Hohenberg and Kohn proof of the bijectivity between the external potential and the basic variable, and the Percus, Levy, and Lieb constrained-search proof. We argue the Hohenberg- and Kohn-type proof to be the more fundamental, and that this is the case in general when both external electrostatic and magnetostatic fields are present, and the basic variables are the ground-state density and physical current density.

Comments

This work was originally published in Physical Review A, available at http://dx.doi.org/10.1103/PhysRevA.85.052502.