📝 SummarXiv

Abstract

We present a direct ab initio solution of the Schrodinger equation for neutral helium and helium-like atoms that reproduces the energies of the singlet S states 1S0, 2S0, and 3S0. 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 4.842 meV, and calculated 2S0 and 3S0 energies show comparable consistency. 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.