Discussion with Eric Scerri on the Periodic Table

Eric Scerri as world expert on the Periodic Table has offered interesting comments to this post asking if the Periodic Table is explained by standard Quantum Mechanics stdQM, in particular if the doubling of periods in the list 2, 8, 8, 18, 18, 32 and 32, is well explained. Scerri says that it has not yet been explained (after 100 years), but that it may be possible. 

The discussion touches the core of stdQM as the fermionic nature of electrons imbedded in anti-symmetric wave functions including a two-valued spin quantum number expressed in the Pauli Exclusion Principle PEP. 

Schrödinger formulated his equation for the Hydrogen atom with one electron in 1926, which gave meaning to quantum numbers introduced earlier and so was a formidable success. Schrödinger hinted at a direct formal extension to Helium with two electrons and so on for many electrons adding new spatial variables, but that model did not work because it made no distinction between bosons and fermions. So was Schrödinger's original model quickly complemented with a requirement that multi-dimensional wave functions must be anti-symmetric as fermions with satisfaction of PEP, which became stdQM. But Pauli was not happy with his PEP, even if it gave him the Nobel Prize in Physics, viewing it to be an ad hoc fix. 

RealQM gives a different generalisation of Schrödinger's so successful equation for the Hydrogen atom, where electrons have identity by occupying different regions of a common 3d space. There is here no need of a PEP nor of a 4th spin quantum number, in the original spirit of Schrödinger and Pauli. Electron configurations appear in RealQM as the result of a packing problem of non-overlapping charge densities. It appears that RealQM can add physics to the Periodic Table with doubling of periods as a natural outcome of electron packing under energy minimisation.