realQM: Helium Ground State -2.9036 = Success

Computation with realQM in spherical coordinates with azimuthal symmetry on a mesh with 200 points in radial direction and 100 in polar angle (on my iPad), gives the value -2.9036... (Hartree) for the ground state energy of Helium in good agreement the observed value and benchmark computations with stdQM (here and here):

• Pekeris (1959): -2.903724376    (best stdQM/Hylleraas with 1078 parameters)
• Koki (2009): -2.9042 (in supposedly better agreement with observation).

realQM offers a new model of the atom, which has a physical meaning in classical continuum mechanical terms and which is computable. The first test of realQM, beyond the one-electron Hydrogen atom where realQM coincides with the standard Schrödinger equation, is Helium with two electrons, and it seems that realQM passes this test successfully! The step from one to two is huge while the step from two to many may be smaller...so if realQM works for Helium, then...

Wikipedia gives the observed value −2.90338583(13) with reference:

• Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team. "NIST Atomic Spectra Database Ionization Energies Data". Gaithersburg, MD: NIST. 

The difference with Pekeris is significant: stdQM does not appear to fit better with observation than realQM...maybe less... Wikipedia handles the discrepancy by the following hand-waving:

• It should be noted that one needs to include relativistic and quantum electrodynamic corrections to get full agreement with experiment to spectroscopic accuracy.

PS1 1st ionisation energy as observed is supposed to be 0.903569881854.

PS2  Nakashima and Nakasuji reports -2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 with 40 correct decimals, still different from observation -2.903385...