Schrödinger’s Equation vs Heisenberg’s Uncertainty Principle

Schrödingers wave equation in a wave function $\Psi (x,t)$  serves as the foundation of quantum mechanics. For an atomic system with $N$ electrons, $x$ is a $3N$-dimensional space variable and $t$ is a time variable. The physical meaning of $\Psi$ has been hotly debated for close to hundred years without ever any agreement being reached, the reason being that the equation for $N>1$ came out as a purely formal generalisation without physical basis of the equation Schrödinger formulated in 1925 for the case $N=1$ from an model of an electron as a form of negatively charged cloud with charge density $\vert\Psi (x,t)\vert^2$. A form of consensus named Copenhagen Interpretation CI to give $\Psi$ a probabilistic meaning has emerged including an agreement to not ask any further questions.  

A different generalisation to $N>1$ into a system of non-overlapping electronic charge density clouds is presented as RealQM. 

The Heisenberg Uncertainty Principle HUP is viewed as a corner stone of quantum mechanics stating that there is limit to the precision of measurements of the position and velocity of a particle. 

It is natural to ask what role HUP serves in either CI or RealQM? HUP concerns particles while CI and RealQM concern waves and there is no clear connection between particles and waves, in particular not between HUP and RealQM. 

It is also a question of what measurements can be performed on atoms. Atomic spectra can be observed as total electronic energies and there is no limit to measurement precision, while local electronic charge densities cannot be observed at all. 

Thus HUP does not seem to say anything about the wave mechanics of RealQM. It is natural to ask if it does say anything about CI?