Operator method in solving non-linear equations of the Hartree-Fock type

TL;DR

This paper employs an operator method to solve Hartree-Fock type equations, deriving ground and excited state energies for polaron and helium atom models, providing new analytical solutions in strong coupling regimes.

Contribution

It introduces an operator approach to solve non-linear Hartree-Fock equations for polarons and helium atoms, yielding explicit energy calculations.

Findings

Polaron ground-state energy: -0.1085128052α^2

Calculated energies for 2s- and 3s-states

Discussion of excited states

Abstract

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.