Classical Analogs of Schrödinger's Equation

RealQM is based on a Schrödinger equation SE in terms of non-overlapping one-electron charge densities with clear physical meaning, which has the form of classical continuum physics and so can be given different interpretations in elasticity, heat conduction and mass distribution. 

Let us start with the case of the Hydrogen atom with one electron with wave function $\Psi (x)$ with $x\in\Re^3$ satisfying as eigenvalue problem:

• $-\frac{1}{2}\Delta\Psi +V\Psi = E\Psi $         (1)
• $-\frac{1}{2}\Delta\Psi = (E-V)\Psi$          (2)
• $-\frac{1}{2}\Delta\Psi = W\Psi$               (3)

where $d=3$, $V(x)=-\frac{1}{\vert x\vert}$, $E$ is an eigenvalue, $W=E-V$ and $\int\Psi^2(x)dx =1$ as normalisation. 

We can give (3) the following alternative interpretation expressing a balance for $\Psi (x)$: 

• straining of an elastic body subject to a force ,
• temperature of a heat conducting body subject to a heat source. 
• mass density of a substance subject to dissipation and production. 

There is a natural extension of these models to reinterpretations of SE for many electrons.