Bound systems of interacting electrons. A step beyond density functional theory

TL;DR

This paper develops a new approach to interacting electron systems using second quantization, deriving operators for stationary states, and applies it to the Helium atom, achieving high accuracy and offering insights beyond traditional density functional theory.

Contribution

It introduces a novel method using ladder operators in second quantization to analyze interacting electrons, providing explicit solutions for the Helium atom and advancing beyond standard density functional theory.

Findings

Achieved 0.63% error in Helium ground state energy

Derived explicit expressions for ground state and density

Method applicable to more complex systems

Abstract

The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy eigenvalues are derived. The method is particularized to the two-electron Helium atom in order to explain it avoiding too much notation. Applying the lowering operator on the ground state must give zero because no state with lower energy does exist. Equations for the ground state and ground state energy are obtained this way and solved, giving closed--form expressions for the ground state, its energy and electronic density of Helium. The theory in its lowest order gives 0.63% error. The application to more complex systems and higher degrees of approximation seems straightforward. The foundations of the density functional theory and how to go beyond it are seen quite clearly.