Quantum Mechanics as Classical Mechanics can be Understood

Feynman: think I can safely say that nobody understands quantum mechanics. 

The crown jewel of the modern physics of Quantum Mechanics QM is the Schrödinger equation for the Hydrogen atom. Complete Success. Schrödinger rocketed to Fame in 1925.

It is possible to view this model also in terms of classical continuum mechanics as an electron charge density $\psi (x)$ in a potential field $-\frac{1}{\vert x\vert}$ generated by a proton kernel at $x=0$ with the electron charge density resisting "compression" like an elastic body. In this setting the ground state $\psi (x)$ minimises the total energy

• $E(\psi ) = PE(\psi ) + KE(\psi)$

where

• $PE(\psi ) = -\int\frac{\psi^2(x)}{\vert x\vert}dx$ is potential energy 
• $KE(\psi )=\int\frac{1}{2}\vert\nabla\psi (x)\vert^2dx$ is compression energy

under the normalisation 

• $\int \psi^2(x)dx =1$. 

More generally, states with larger energy emerge as stationary points of $E(\psi )$ with corresponding eigenvalues and form the spectrum of the Hydrogen atom in full agreement with observations. 

The connection to the spectrum is realised by extending the real-valued $\psi (x)$ into a complex-valued function $\Psi (x,t)=\exp(-iEt)\psi (x)$ also depending on a time variable $t$ with $E$ an eigenvalue, satisfying Schrödinger's equation in the form 

• $i\frac{\partial\Psi}{\partial t}=H\Psi =E\Psi$ 

where 

• $H = -\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$

is the Hamiltonian differential operator with eigenvalue $E$. All of this makes perfect sense with the Hydrogen atom modeled by classical continuum mechanics with a static electron distribution around a kernel. In particular, nothing is moving fast and so the Dirac equation with all its complexity from being relativistically correct has no role to play.

The novelty of QM came from viewing the electron compression energy instead as a form of "kinetic energy" arising from a purely formal association of classical Newtonian momentum as mass times velocity, with the differential operator $i\nabla$ with respect to $x$, which generates the Laplacian in the Hamiltonian $H$. 

The terminology "kinetic energy" connects to the Bohr model of the atom with electrons as particles orbiting around a kernel like planets around a Sun. But the Bohr model cannot explain the stability of the ground state since orbiting electrons radiate and loose energy.  The "kinetic energy" attributed to a static electron charge density is the root of the mystery of standard QM obsessed with "electron orbitals". 

A further step away from classical mechanics is taken in stdQM as the standard extension of Schrödinger's equation to atoms with mor than one electron, which is also performed as a formality replacing physical space with configuration space without physical meaning, and as a result resorting to statistics. 

RealQM gives a different extension as classical continuum mechanics in terms of non-overlapping electron charge densities subject to mutual Coulomb repulsion but no self-repulsion.

With the Schrödinger equation for the Hydrogen atom cashed in as a complete success, the main question is how to extend it to atoms with more than one atom while keeping the success. 

In stdQM the extension is made as a formality without real physical rationale into a new form of physics as quantum mechanics conceptually different from classical mechanics, thus creating mystery upon mystery.

RealQM makes the extension within classical continuum physics and thus keeps physical rationale without mystery. 

There is a clear choice: Either the atom can be understood, and then in terms of classical physics, or the atom cannot be understood at all.