RealQM vs StdQM: Two-Valuedness of Helium

Real Quantum Mechanics RealQM is an alternative to textbook Standard QM StdQM. Both start with Schrödinger's equation for the Hydrogen atom with one electron, but offer different generalisations to atoms with more than one electron. 

The split between StdQM and RealQM thus takes place for Helium with two electrons. 

The electron configuration by StdQM is fully spherical symmetric with two electrons with different spin occupying identical spherically symmetric orbitals with zero electric dipole moment (and zero magnetic moment). 

In RealQM, which does not include spin, the two electrons occupy different half-spaces meeting at a plane through the nucleus with random orientation and so carries a randomized dipole moment, which could average to zero over many atoms. A collection of Helium atoms can thus according to RealQM be polarized by an exterior electric field and so form an induced dipole. Observations show such an effect. 

It is also possible that an induced dipole can be formed from the full spherical symmetry of StdQM, but then probably weaker. Maybe it is possible to detect such a difference, but this has not been put on the table, because RealQM is still in its infancy.

The split between StdQM and RealQM for Helium connects to the observed two-valued atomic electron configurations as the basis for the Periodic Table PT: StdQM introduces two-valued spin, while in RealQM two-valuedness is the result of the split of the two electrons of Helium into two separate half-spaces, which carries through when outer half-shells are added. StdQM says two-valued spin, RealQM says two-valued half-space geometry.

Observed two-valuedness in the PT was the origin to Pauli's Exclusion Principle PEP, which appeared as an ad hoc fix but is now accepted as a deep physical principle included in StdQM. In RealQM electrons occupy different regions of 3d space and two electrons sharing domain is not an issue.  

It may be that the strong consensus around StdQM has prevented closer experimental investigation of presence of induced electric dipole since in StdQM this is expected to be very weak. Maybe such a study can be motivated if RealQM is seen as a possible alternative to StdQM. 

In any case, RealQM suggests that the ground state of Helium has a randomized dipole moment which may help to form an induced dipole. 

PS A closer discussion with chatGPT shows a distinction between isotropic polarizability connecting to StdQM with London dispersion forces, and random dipoles connecting to RealQM with Keesom forces. It is possible that observations favour London before Keesom but maybe expectations play a role...

 

The Mysterious Two-Valuedness of Spin Quantum Mechanics

Once Schrödinger in 1926 had formulated his partial differential equation for the Hydrogen atom with one electron with an eigenvalue spectrum in full agreement with observation, the next challenge was the Helium atom with two electrons: How to generalise from one to many electrons? 

The way to to do this was not clear and the simplest option was followed: Make a formal mathematical generalisation with a stroke of a pen, just add a new 3d spatial coordinate for each new electron to form Schrödinger's multi-dimensional wave equation in $3N$ spatial dimensions (plus time) for an atom/molecule with $N$ electrons, and then seek to live with that equation. The trouble still haunting modern physics is that the physical meaning of Schrödinger's equation is still hidden if any at all, despite intense efforts over 100 years.  

For the Helium atom with two electrons this gives a six-dimensional wave equation, with the ground state appearing as having minimal energy. But what is the electron configuration of that state? The idea then came up, from the success for the Hydrogen atom, to view the ground state of Helium to be composed of two spherically symmetry Hydrogen-type wave functions with the electrons so to speak on top of each other.  To make that possible in view of the Coulomb repulsion between electrons, Wolfgang Pauli suggested to assign the electrons different values of "spin" as "spin-up" and "spin-down" and then postulate a Pauli Exclusion Principle PEP proclaiming that two electrons with different "spin" can share spatial domain. 

The ground state of Helium was thus declared to be a $1S^2$ state with two identical spherically symmetric electron charge distributions with different spin, which gave a rough fit with observation. 

Pauli himself viewed PEP to be a mistake, but the physics community happily adopted the idea of a two-valuedness of quantum mechanics in the form of "spin-up" and "spin-down", which is now firmly implanted in Standard Quantum Mechanics StdQM.

In RealQM, as an alternative to the formal generalisation of StdQM into many electrons, the two-valuedness of Helium takes a different form as a split of the two electrons to be restricted to half-spaces meeting at a plane through the kernel. This a physical split of charge distribution to be compared with the formal split of StdQM into "spin-up" and "spin-down".

In RealQM the separating plane gives the charge distribution a direction in space, which is lacking with only "spin-up" and "spin-down".

The previous post takes up possible physical effects of the RealQM electron split in the form of diamagnetism. 

RealQM presents a physical origin to the observed two-valuedness of He, which is independent of any PEP. There is no PEP in RealQM because it serves no need, and so can be dispensed. 

Pauli would have been very satistfied with this message, but quantum mechanics has continued to cling to PEP as the correct expression of two-valuedness. 

Since all atoms have an innermost shell of two electrons, and maybe also an outermost, RealQM for any atom carries a form of two-valuedness, which is not based on two-valued spin.

RealQM with electrons split into two half-spaces gives a ground state energy which fits better with observations than the $1S^2$ configuration with split spin. Does that say anything?

 

New Quantum Mechanics 11: Helium Mystery Resolved

The modern physics of quantum mechanics born in 1926 was a towering success for the Hydrogen atom with one electron, but already Helium with two electrons posed difficulties, which have never been resolved (to be true).

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))

Text books and tables list the ground state of Helium as $1S^2$ with two spherically symmetric electrons (the S) with opposite spin in a first shell (the 1), named parahelium.  The energy of a $1S^2$ state according to basic quantum  theory is equal to -2.75 (Hartree), while the observation of ground state energy  is -2.903. To handle this apparent collapse of basic quantum theory, the computation of energy is changed by introducing a suitable perturbation away from spherical symmetry which delivers the wanted result of -2.903, while maintaining that the ground state still is $1S^2$.

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:

Notice the asymmetric electron potential and the resulting slightly asymmetric charge distribution with polar accumulation. The model shows a non-standard electron configuration, which may be the true one (if there is anything like that).