Exact phase space functional for two-body systems

TL;DR

This paper derives an exact phase space functional for two-body systems within Moshinsky's harmonium model, resolving the phase dilemma through a phase-space approach and energy minimization.

Contribution

It introduces an exact phase space functional for two-body systems and resolves the phase dilemma using a novel phase-space formulation.

Findings

Derived the two-body density functional from one-body density

Resolved the phase dilemma in the harmonium model

Established sign rules via energy minimization

Abstract

The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.