Kinetic Energy in Quantum Mechanics Without Kinetics

Schrödinger's equation as the fundament of Quantum Mechanics in its standard form as StdQM is not derived from physical principles but from a mathematical formality replacing momentum $p=mv$ with $m$ mass and $v$ velocity of classical mechanics with $i\nabla$ with $\nabla$ spatial gradient operator with respect to a space coordinate $x$ and so postulating the (total) "kinetic energy" of a quantum particle of mass $m$ with wave function $\psi (x)$ to be, with Planck's constant normalised to 1: 

• $\frac{1}{2m}\int\vert\nabla\psi (x)\vert^2dx$         (1)

as a formal analog of the kinetic energy of a classical particle with momentum $p=mv$ given by

• $\frac{1}{2m}\vert p\vert^2=\frac{m\vert v\vert^2}{2}$.                          (2).

So is the Schrödinger equation "derived" by a formal mathematical operation of replacing momentum as number by the operator $i\nabla$, which does not make much sense from a physical point of view. In particular, the presence of the mass $m$ in (1) lacks physics. 

The result is confusion: StdQM says that an electron is not a particle orbiting an atomic kernel, but yet it is in StdQM attributed to have mass and kinetic energy as if is a moving particle. 

In RealQM an electron in an atom/molecule is a charge density occupying a certain domain in space, given by a function $\psi (x)$, which can vary over time but is not moving around with kinetic energy. In RealQM the gradient $\nabla\psi (x)$ can be interpreted as a form of "strain" with (total) "strain energy" given by (some multiple of)  

• $\int\vert\nabla\psi (x)\vert^2dx$                             (3)

to be compared with (1). 

Electron mass is not an element of RealQM, nor is relativistic electron speed.

The physics of StdQM is still not understood 100 years after its conception. The physics of RealQM is understandable in the same sense as classical continuum mechanics. RealQM connects to Hartree-Fock/DFT and QTAIM all based on StdQM, by involving distribution of charge densities in space, but RealQM is not based on StdQM and so is fundamentally different. 

The unsolvable dilemma of StdQM is that it is based on an idea of electron as particle, which is refuted by  lacking physics and then twisted into an idea of electron as probability density again without physics.  

RealQM offers an aternative as physics of charge densisties. 

StdQM is based on mathematics that does not make sense, e g kinetic energy without kinetics.

RealQM is based on mathematics that makes sense: charge density, Laplacian, Bernoulli free boundary.