Analytical solution of the Schrodinger equation for the neutral helium atom in the ground state considering the uncertainty principle, vibrational modes and quantum-electrodynamical effects

TL;DR

This paper develops an analytical method to solve the Schrödinger equation for the helium atom's ground state, incorporating quantum effects, vibrational modes, and QED corrections, achieving high accuracy and explaining chemical inertness.

Contribution

It introduces a novel analytical approach using complex analysis and Laplace transforms to solve the two-electron problem with quantum corrections.

Findings

Ground-state energy matches literature within 1.86 meV

Provides an analytic description of entangled electrons in helium

Accounts for helium's chemical inertness and spatial structure

Abstract

We present a direct ab initio solution of the Schrodinger equation for neutral helium and helium-like atoms that reproduces the energy of the singlet S state 1S0. By redefining the two-electron wavefunction with tools from complex analysis and solving the S=L=0 problem via Laplace transforms, we derive an analytic description of the entangled electrons. To respect Heisenbergs uncertainty principle while retaining pointlike electrons, we introduce an adapted, generic electron potential and incorporate it into the equations. Perturbative dark electronic vibrational modes, Breit-Hamiltonian corrections, and QED effects (including the Lamb shift) are included. The ground-state energy agrees with literature within 1.86 meV. The framework also accounts for heliums chemical inertness (closed shell) and yields spatial structure parameters in reasonable accord with reported values, providing an analytic route to describing helium.