Basic Formalism for Stationary Non-Relativistic Systems

Abstract

We start with a short summary of the original version of the Hohenberg-Kohn theorem (1964) which was formulated for local, spin-independent external potentials leading to a non-degenerate ground state. The question of degenerate ground states is considered in the following subsection. The formulation of the basic theorem has led to a substantial body of literature (for recent reviews, see, e.g., Lieb, 1982, and Erdahl and Smith, 1987) addressing its rigorous mathematical foundation. This subject will be covered from a physicist’s point of view in the section on v-representability. Finally we shall describe an extension of the formalism to fractional particle number which leads to the recently discovered derivative discontinuities of the fundamental energy functional.