Physics of RealQM in Nutshell

Real Quantum Mechanics RealQM offers a generalisation (newS) of Schrödinger's equation (S) for the Hydrogen atom with one electron from 1926, to atoms and molecules with $N>$ electrons, in the form of a system of one-electron wave functions with non-overlapping supports representing non-overlapping charge densities in 3d, which has a clear physical meaning. The computational complexity of (newS) scales linearly with $N$, which makes solutions computable for large $N$.

This is different from the generalisation by formal mathematics coming to serve as the foundation of modern physics in the form of Standard Quantum Mechanics StdQM, obtained by adding a new 3d coordinate system for each new electron, thus forming a multi-dimensional Schrödinger equation (oldS) in $3N$ spatial dimensions for a system with $N$ electrons, without direct physical meaning. The computational complexity of (oldS) scales exponentially with $N$, which makes solutions to (oldS) uncomputable already for $N$ bigger than 5. 

We compare:

• (newS) has physical meaning and is computable for even for large number of electrons.
• (oldS) has no direct physical meaning and is uncomputable already for small number of electrons. 

I have reported on many cases in this book and on this blog showing fair/good agreement of computed solutions to (newS) with observations, typically atomic ground state energies, atomic ionization energies and molecular dissociation energies. The computations were performed on an iPad on a 3d mesh with 1 million mesh points as an iterative energy minimisation explicit update in a code with essentially three lines. 

In general the results using (newS) agree with those reported in the literature using (oldS) with both results in fair/good agreement with observations. RealQM based on (newS) offers quick computation with physical meaning, to be compared with StdQM based on (oldS) demanding heavy computation without direct physical meaning. 

Let us recall the essence of (newS) coming to expression in a 3-line computer code:

1. (newS) is a system of partial differential equations in terms of one-electron wave functions with non-overlapping supports representing non-overlapping charge densities.
2. Each wave functions seeks to minimise its energy subject to Coulomb potentials from the other electrons and the kernels  
3. Wave functions meet at a free boundary with continuity of wave functions and zero normal derivates as a Bernoulli free boundary.
4. The free boundary is updated using a level set method. 

The 3-line code consists of update of (i) wave functions, (ii) electron potentials and  (iii) free boundary.

Since charge densities of (newS) do not overlap, there is no need to involve electron spin, nor Pauli Exclusion Principle. 

RealQM offers a new view on chemical bonds as essentially all covalent with the Bernoulli free boundary serving a key role by allowing electrons to accumulate between kernels resulting in energy drop from kernel potentials without increase of kinetic energy.