While electron and proton being far apart are allowed to be imagined as nearly point particles, when they approach ~10^-10m (or much more for Rydberg atoms), electron is said "to become" this relatively huge wavefunction - orbital, describing probability distribution of finding electron (confirmed experimentally e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 ).

Can we specify in what e-p distance this qualitative change happens?

How to think about this orbital from QM interpretations perspective - is it superposition of electron (indivisible charge) being in all these places?

E.g. in Many Worlds Interpretation, should we imagine that electron has different position in each World?

In such superposition each electron is staying or moving? If staying, where e.g. the orbital angular momentum comes from? If moving, why no synchrotron radiation?

In other words: is electric field of orbital a superposition over electron being in all places, or rather mean?

11 hours ago, Duda Jarek said:

While electron and proton being far apart are allowed to be imagined as nearly point particles, when they approach ~10^-10m (or much more for Rydberg atoms), electron is said "to become" this relatively huge wavefunction - orbital, describing probability distribution of finding electron (confirmed experimentally e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 ).

Can we specify in what e-p distance this qualitative change happens?

How to think about this orbital from QM interpretations perspective - is it superposition of electron (indivisible charge) being in all these places?

E.g. in Many Worlds Interpretation, should we imagine that electron has different position in each World?

In such superposition each electron is staying or moving? If staying, where e.g. the orbital angular momentum comes from? If moving, why no synchrotron radiation?

An orbital is not an electron and vice versa.

An electron is a physical phenomenon that can be interacted with.

An orbital is a mathematical description of a region of space defined not only by a  general equation (the Schrodinger equation) but also by assiciated boundary conditions.

The equation is the same (although coefficient values are different) but the boundary conditions are very different for the near and far situations you describe.

The nucleus is not a point, and this fact is responsible for some of the energy structure of the atom  

Neutral atoms do not have a net charge or an electric dipole moment. So you run into a problem if your model has the electron at a specific point, which gives you an EDM.

Electron has associated electric field, so asking about electric field of atom/orbital, is it superposition of electric field of electron being in each point, or maybe mean?

For example placing another atom nearby, should their electrons somehow synchronize (e.g. van der Waals force)? Don't it require superposition?

The analyses I’ve seen look at energy, not electric field. The force isn’t what goes into Schrödinger’s equation 

Sure, we can ask it using potential energy, e.g.: charged particle near atom behaves accordingly to superposition of Coulomb potential of electron being in all points, or maybe accordingly to single Coulomb potential: averaged over wavefunction?

When you operate on the hydrogen wave function with the Hamiltonian you get the energy levels. The wave function exists in all space. You don’t need to average; you just need to include the equation of the potential 

On 10/19/2020 at 1:04 AM, Duda Jarek said:

In such superposition each electron is staying or moving? If staying, where e.g. the orbital angular momentum comes from? If moving, why no synchrotron radiation?

The system can only radiate if it has a lower energy state available (i.e. consistent with the selection rules). It won’t radiate continuously.