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...

 

Orthohelium Alternative Electron Configuration

In the previous post we let RealQM compute the first line in the spectrum of Helium from ground state as Orthohelium assuming that one electron is excited from 1S to 2S and obtained an energy of 0.728 Hartree in accordance with observation as a line easy to observe as the difference between $-2.175$ and $-2.903$ Hartree. 

We compare assuming instead excitation to the 2nd eigenvalue of Schrödinger's equation for Helium in the form given by RealQM. You can run the code here. We obtain the same energy of 0.728 Hartree in agreement with observation. 

RealQM thus gives the same first line in the spectrum of Helium with two different electron configurations.

Note that in Standard Quantum Mechanics StdQM the first exited states of Helium comes on two forms, as Orthohelium with the the two electrons having the same spin as a triple state, and Parahelium with different spin as a singlet state. RealQM corresponds to Orthohelium since in RealQ there is only same spin. 

Orthohelium is much easier to observe (more stable) than Parahelium and so appears to represent more solid physics. 

The fact that RealQM gives correct 1st line of Helium as Orthohelium with two different electron configurations is another piece of evidence that RealQM captures physics. Both configurations have in the RealQM electric dipoles varying over time and so radiate, with the 1S to 2S weaker.

The electron configuration of Orthohelium in StdQM is very complex, and as such probably with less physics. 

Recall that DFT being focussed on ground states has to struggle with excited states in heavy software. It may show to be remarkable that the 3-line code of RealQM can outperform DFT.

 

RealQM Spectrum of Helium: 1st Excited State as Orthohelium

We now explore the spectrum of Helium delivered by RealQM. The spectrum of an atom primarily reflects energy differences between the ground state and excited states, but also between excited states.

Standard Quantum Mechanics StdQM presents the first exited state of the Helium atom with two electrons to be a singlet state with the two electrons having opposite spin named Parahelium, but there is also a triplet state with the electrons having same spin named Orthohelium. 

The first line in the spectrum of Helium (smallest energy jump from ground state) corresponding to an energy of $-2.175$ Hartree is that of Orthohelium, compared to $-2.903$ for the ground state, while Parahelium has 0.03 higher energy of $-2.145$ Hartree. 

Let us see what RealQM delivers. Since in RealQM all electrons have the same spin, RealQM connects to Orthohelium giving the first line in the spectrum. We let RealQM model this state with one electron around the kernel and the other electron in an excited state outside. You can here run the code to find that RealQM gives an energy of $-2.175\pm 0.005$ Hartree depending on iteration stop criterion. 

We thus see that RealQM gives a result in agreement with observation of the 1st line in the spectrum of Helium in the form of a very simple arrangement of the two electrons: An inner electron around the kernel and an outer electron around the kernel + inner electron. Run code to see. The corresponding triplet state of StdQM is very complicated:

Orthohelium corresponds to the first line in the Lyman series for Hydrogen (with drop of wave length from 122 nm to 62.6 nm), with details on further lines to come.

PS The ground state of Helium with its two electrons overlapping with opposite spin in StdQM, is in RealQM modeled with the electrons split into halfspaces without overlapping. See this code. The transition to excited state in RealQM is thus from a state of half space split electrons into a state with spherically symmetric electrons, one inner and one outer, which appears to require a quite precise excitation input.