StdQM as Black Box vs RealQM

RealQM as an alternative to textbook Standard Quantum Mechanics StdQM is now under review for publication in Foundations of Chemistry. To prepare for the expected questioning of the need of any alternative whatsoever, let me recollect some basic facts about the present role of StdQM as foundation of atomic physics and of chemistry as based on atomic physics.

StdQM for an atomic system $S$ with $N$ electrons is based on a linear Schrödinger Equation SE defined by a Hamiltonian $H$ with solution $\Psi (x_1,x_2,...,x_N)$ named wave function depending on a $N$ 3-dimensional spatial coordinates $x_i$ each representing one electron. The spectrum of $S$ is given as the set of eigenvalues $E$ of $H$ with corresponding eigenfunctions $\Psi=\Phi$ satisfying 

• $H\Phi =E\Phi$. 

The smallest eigenvalue is the ground state energy of the system. The spectrum can in principle be computed by solving the eigenvalue problem, which acts like a black box delivering eigenvalues $E$ and eigenfunctions $\Phi$, while not displaying the real physics behind because the wave function depends on $3N$ spatial variables which is not physical space for $N>1$. Moreover, the computational complexity is exponential in $N$, which makes the computation hypothetical. 

We see that StdQM can be viewed to act as a hypothetical black box which delivers eigenvalues based on eigenfunctions without clear physical meaning. Something essential appears to be missing. Is there any alternative? 

Note that there is no probability involved so far. It enters as a (desperate) attempt give the multi-dimensional wave function $\Phi$ some physical meaning, but it comes along with fundamental problems which have never been resolved despite 100 years of intense search. The black box still appears fundamentally non-transparent.   

We now compare with RealQM which is based on a different SE but essentiall the same Hamiltonian with wave functions $\psi (x) =\sum_{i=1}^N\psi_i (x)$ depending on a physical 3d coordinate $x$, as a sum of one-electron wave functions $\psi_i(x)$ with non-overlapping supports and $\psi_i^2(x)$ representing charge density. 

RealQM also delivers spectrum as eigenvalues with now eigenfunctions expressing distribution of non-overlapping electron charge densities. RealQM thus reveals the physics inside a box delivering spectrum. The computational complexity is linear in $N$. 

We sum up: 

• StdQM delivers spectrum as black box without physics with exponential complexity. 
• RealQM delivers spectrum as transparent box with physics with linear complexity. 

Does RealQM have a role to serve as alternative to StdQM?