Hartree-Fock approximation for non-Coulomb interactions in three and two-dimensional systems

TL;DR

This paper investigates the Hartree-Fock approximation applied to electron systems with non-Coulomb interactions in 2D and 3D, providing analytical results and extending classical Coulomb-based findings.

Contribution

It introduces analytical solutions for non-Coulomb interactions in electron systems, generalizing classical Coulomb results to new interaction potentials.

Findings

Analytical expressions for particle energy and velocity

Ground state energy calculations for non-Coulomb systems

Extension of classical Coulomb results as special cases

Abstract

We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate analytical results for the particle energy, the particle velocity, the ground state energy of the system as well as the momentum dependent density of states. The previous classical results for the Coulombian case were reobtained as particular cases.