Real Quantum Mechanics RealQM offers a continuum mechanical mathematical model of an atom as a system of non-overlapping one-electron charge distributions around a kernel of charge Z with electrons meeting with a Bernoulli free boundary condition (continuity + homogeneous Neumann condition).
The electrons organise in shells with 2*n*n electrons in shell n if filled giving the observed pattern of 2, 8, 18, 32 electrons in fully filled shells. The factor 2 comes from a two-valuedness for the Helium atom expressed by two electrons separated by a plane through the kernel as the free boundary.
Watch DigiMat illustration of the shell structure as Atom Secret.
RealQM is computable as a system of differential equations in 3 space dimensions. RealQM is to be compared with the standard quantum mechanical model as Schrödingers’s equations in 3N space dimensions for an atom with N electrons, which is not computable unless N is very small.
You find several examples of RealQM in Model Workshop. In particular play with RealQM Atom Simulator.