Schr\"odinger equations for the square root density of an eigenmixture and % the square root of an eigendensity spin matrix

TL;DR

This paper extends a theorem relating to eigenstate densities to eigenmixture densities, with implications for radial density functional theory in nuclei, and explores Schr"odinger equations for spin eigendensity matrices.

Contribution

It generalizes the LPS theorem to eigenmixture densities and investigates Schr"odinger equations for spin eigendensity matrices in nuclear RDFT.

Findings

Generalization of the LPS theorem to eigenmixture densities

Derivation of Schr"odinger equations for spin eigendensity matrices

Application to radial density functional theory for nuclei

Abstract

We generalize a "one eigenstate" theorem of Levy, Perdew and Sahni (LPS) to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei, a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the RDFT uses eigenmixture density operators to simplify predictions of GS energies into one-dimensional, radial calculations. We also study Schr\"odinger equations governing spin eigendensity matrices.