Atom energy band formation and electron allotment

[Clueless123]

This is actually a two-part question:

1) According to the Copenhagen Interpretation, atoms have energy bands but there's no explanation of how these bands are derived, or why they only form for protons/antiprotons. Any thoughts?

2) The Copenhagen Interpretation mentions that when an atom's energy band has a full allotment of electrons, the energy band neutralizes that prevents additional electrons from entering (to ensure a one-to-one pairing with protons). Is there a detailed, step-by-step explanation of how this neutralization process manifests by the atom? Of how the additional electrons are prevented from entering the band?

 

[renormalize]

This is actually a two-part question:

1) According to the Copenhagen Interpretation, atoms have energy bands but there's no explanation of how these bands are derived, or why they only form for protons/antiprotons. Any thoughts?

2) The Copenhagen Interpretation mentions that when an atom's energy band has a full allotment of electrons, the energy band neutralizes that prevents additional electrons from entering (to ensure a one-to-one pairing with protons). Is there a detailed, step-by-step explanation of how this neutralization process manifests by the atom? Of how the additional electrons are prevented from entering the band?

What references are these statements based upon?

 

[Nugatory]

This is actually a two-part question:

For the first question, I have no idea what you're talking about when you say "...only form for protons/antiprotons". If you could tell us what source you're using for this statement we might be better able to understand the question.
For the second question, atomic energy levels and the shell filling rules appear when we solve Schrödinger's equation for electrons bound in an atom (although when we do this exercise in our first-year QM class we take the exclusion principle as an additional assumption - the rigorous proof of that comes a few years later). So the step-by-step explanation is the step-by-step solution to Schrödinger's equation.

The Copenhagen interpretation has pretty much nothing to do with any of this.

In one of your other threads a week or so ago I suggested that you might want to try Ghirardi's book. That was good advice then and it still is.

 

[PeterDonis]

According to the Copenhagen Interpretation

The Copenhagen Interpretation

Discussions of particular interpretations of QM belong in the interpretations subforum, not this one.

However, it does not appear that your actual questions have anything to do with any particular interpretation. They look like straightforward questions about experimental predictions of QM, which are independent of any particular interpretation.

 

[Vanadium 50]

However, it does not appear that your actual questions have anything to do with any particular interpretati

Or reality.

Single atoms have energy levels. Bulk matter has energy bands.

 

[vanhees71]

This is actually a two-part question:

1) According to the Copenhagen Interpretation, atoms have energy bands but there's no explanation of how these bands are derived, or why they only form for protons/antiprotons. Any thoughts?

The physics is independent of the interpretation (or only dependent on the minimal interpretation needed to connect the abstract mathematical formalism of QT with real-world observations). According to QT an atom is described by a Hamiltonian, which has a spectrum which has a discrete part (describing "bound states") and a continuous part (describing "scattering states"). There are no "energy bands". This is a notion related to macrocopic matter, particularly solid bodies/crystals.

2) The Copenhagen Interpretation mentions that when an atom's energy band has a full allotment of electrons, the energy band neutralizes that prevents additional electrons from entering (to ensure a one-to-one pairing with protons). Is there a detailed, step-by-step explanation of how this neutralization process manifests by the atom? Of how the additional electrons are prevented from entering the band?

Again this has nothing to do with whatever interpretation of QT you use. If I understand your pretty vague ideas right, you are referring to the Pauli exclusion principle, which is valid for fermions, and electrons are fermions. It says that the many-electron wavefunctions are completely antisymmetric under exchange of any two electrons. This implies that no single-electron states can be occupied with more than one electron, and this leads to the "shell structure" of the atoms.