Update of Real Quantum Mechanics: Electron vs Kernel

I have made a discovery resolving an issue with poor correspondence between theory and observation in the new approach to quantum mechanics termed realQM presented here and here and here.

In the original setting of realQM the same set-up was used as in the standard version of quantum mechanics based on the Schrödinger equation as concerns the kernel assumed to act like a point source with no extension with a corresponding potential $-Z/r$ with $Z$ the kernel charge and $r$ the distance to the kernel, thus with a singularity at the kernel with $r=0$.

In this setting realQM gave a ground state energy for Helium (with two electrons meeting the kernel) of about -3.0 which was substantially lower than the observed -2.9034.

Something was thus wrong with realQM in this original form, and I could not figure out what. I have now understood that this mismatch comes from the kernel singularity which, like all singularities, introduces a dark horse into the model, which has to be handled properly to not lead astray. It is thus natural to give the kernel a positive radius and study the dependence of the ground state energy on the kernel radius.

The question of the boundary condition for the electron as it meets the kernel at a positive radius then comes up, something which is hidden if the radius is zero. Recalling that the boundary condition on the free boundary separating different electrons is a homogeneous Neumann condition, it is natural to try the same condition for the kernel, understanding that it requires the kernel to have positive radius.

An alternative is to use a Robin boundary condition of the form $\frac{\partial\phi}{\partial r}=-Z\phi$ for a positive radius. This is the effective condition at zero radius built into the Schrödinger equation with a point source kernel.

And indeed, both approaches seem to work (very similarly) as recorded in the above references.

More specifically, the kernel radius (which comes out to be small (of size 0.05 - 0.01 atomic units for kernel charge 2-10) can be used as a model parameter, which can be adjusted to give exact agreement with observations as a calibration of the realQM model for two electron ions, which can serve to build a model with more electrons in outer shells.

The model of realQM thus opens to inspection of the inner mechanics of an atom, including information on the effective radius of the kernel as seen by an electron in the innermost shell, something which is hidden to direct experimental observation.

We recall that standard quantum mechanics stdQM does not offer a physical model of the atom and thus with stdQM the inner mechanics of an atom is closed to human understanding, a defect made into a virtue in the Copenhagen interpretation of stdQM filling text books.