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Currently there are two main ideas of those electrons that move in a conductor:

  1. those electrons moving are loosely bound to the valence shells of the atoms in the lattice

  2. those electrons moving are delocalised

Now for 1. these questions are saying they are loosely bound:

Do electrons move around a circuit?

Why can an electrons initial kinetic energy be considered negligible in the photoelectric effect?

where annav says:

The photons will at first meet the surface of the metal, where the first thing they interact with is the conduction band electrons that are very loosely bound, and thus have small average kinetic energy to contribute to the interaction.

What does the concept of "free electron" mean in the context of band theory?

where Sinkfly says:

In fact, in my introductory solid-state physics book, the additional electron contributed by a donor in a doped semiconductor is referred to as "loosely bound" to the donor ion, requiring a push into the conduction band to break free and become a charge carrier.

Now for 2. these questions say they are not loosely bound but they are delocalised:

How does electricity travel near the speed of light if electrons drift at a snail pace?

where my2cts comments say:

Electrons are never bound to shells. - "The electrons can move thus from one atom to the other atom's valence shell. " No they don't. They are delocalised. -

Question:

  1. Which one is right? Are electrons (that move) in a conductor loosely bound to the valence shells of the atoms or are they delocalised? I am asking for a QM level explanation.
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  • $\begingroup$ Are you familiar with Bloch states and the Kronig-Penney model? $\endgroup$ – user3518839 Mar 30 at 5:09
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As is observed in quantum oscillations experiments, metals have well-defined Fermi surfaces. This tells us that conduction electrons in metals form a Fermi liquid. The lattice potential influences the shape of the Fermi surface, and lattice phonons may interact with the Fermi quasiparticles, but the liquid is not localized by the lattice potential in the absence of disorder.

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  • $\begingroup$ Can you please tell me if the electrons are in your answer loosely bound to the valence shells or not? $\endgroup$ – Árpád Szendrei Mar 30 at 15:21
  • $\begingroup$ The electrons are spatially delocalized. $\endgroup$ – d_b Apr 5 at 3:05
  • $\begingroup$ So you are saying they are not loosely bound to the valence shells? $\endgroup$ – Árpád Szendrei Apr 5 at 3:20

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