Particle Correlations in the Generalized Thomas-Fermi Approach

TL;DR

This paper extends the Thomas-Fermi approach to include particle correlations in quantum many-body systems with non-Coulomb interactions, using integral equations to account for interactions beyond weak coupling.

Contribution

It introduces a generalized Thomas-Fermi method that incorporates particle correlations through an integral formulation and pair distribution functions.

Findings

Derived an integral equation for the pair distribution function.

Reduced to Bogoliubov's equation in the classical limit.

Provides a framework for non-perturbative interaction analysis.

Abstract

This paper presents the Thomas-Fermi approach generalized to consider the particle correlations in many-body systems with non-Coulomb interaction potentials. The key points of the generalization consist in using integral formulation and extracting the pair distribution function. The latter has been found to obey the integral equation which, in the classical limit, is reduced to the well-known equation of Bogoliubov. So, the approach presented gives the way of taking into account interactions in the quantum many-body systems beyond the weak coupling perturbation theory.