A density functional perspective for one-particle systems

Abstract

Density functional theory is discussed in the context of one-particle systems. We show that the ground state density ${\rho }_0(x)$ and energy $E_0$ are simply related to a family of external potential energy functions with ground state wave functions ${\psi }_n(x)\propto {\rho }_0(x{)}^n$ and energies $E_n=2n{E}_0$ for certain integer values of $n$.

7 pages, ReVTeX4, submitted to Am. J. Phys