On the Validity of Janak’s Theorem and Ground State Energies of Ensembles of Interacting Quantum <i>N</i>-Particle Systems

Abstract

It is established that for finite number of electrons, N < ∞ , and in the limit T = 0 , the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, E v [ N ] , of an interacting N -particle system under an external single-particle potential, v ( r ) , is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.