The result is that prominent physicists always pride themselves by stating that quantum mechanics cannot be understood, only be followed to the benefit of humanity, like a religion:
- I think I can safely say that nobody understands quantum mechanics. (Richard Feynman, in The Character of Physical Law (1965))
Of course, this does not make sense, but since quantum mechanics is not "anschaulich" or "visualisable" (as required by Schrödinger) and therefore cannot be understood by humans, this is not a big deal. By a suitable perturbation the desired result can be reached, and we are not allowed to ask any further questions following the dictate of Dirac: Shut up and calculate.
New Quantum Mechanics resolves the situation as follows:
The ground state is predicted to be a spherically (half-)symmetric continuous electron charge distribution with each electron occupying a half-space, and the electrons meeting on at plane (free boundary) where the normal derivative for each electron charge distribution vanishes. The result of ground state energy computations according to earlier posts shows close agreement with the observed -2.903: