On the Hartree-Fock Eigenvalue Problem

TL;DR

This paper introduces a novel formulation of the Hartree-Fock eigenvalue problem by transforming it using harmonic function properties, aiming to simplify the problem and enable new approximation methods.

Contribution

It presents a new approach that eliminates the Laplacian from the Hartree-Fock eigenvalue problem, potentially simplifying solution techniques.

Findings

New formulation reduces problem complexity

Potential for improved approximation methods

Facilitates analytical and numerical solutions

Abstract

Using properties of harmonic functions in multidimensional space, we transform the Hartree-Fock eigenvalue problem into a more tractable eigenvalue problem in which the Laplacian is eliminated. This new formulation may facilitate the development of novel ways of finding approximate solutions of the electronic problem.