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I want to fully understand the electron gas but I am sometimes confused about its behaviour, due tho its models.

So the materials like metals got its ionts periodically arranged in the crystal lattice making an organised structure and in this structure we have also a "cloud" of "free" electrons, that's why metals are also the conductors. But then we have an infinite potential well model. Hence the electron is restricted by its discrete energy levels. The potential is zero inside the well and infinite on the outside - the electron without external forces cannot escape the well and must be inside the well. We then can calculate from the Schrodinger equation the possible states of the electrons. So its position is also restricted. But it is just a model for its energies, righ? I have problem to imagine a cloud full of electrons where the electrons actually have some given positions (I don't mean the electron is sitting, that is not possible, but there are places where it is more likely to be, like inside of the atom). So what the free electrons do inside of the metal? I don't mean just collisions if those collisions dont explain the potential model.

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  • $\begingroup$ And Harsh suggest, in solid you not longer assume that you have an infinite potential well, but you look at the interaction between the all (or at least nearby) electrons and nuclei. You are about to deep dive into Band Theory $\endgroup$ – user190081 Sep 10 '18 at 18:24
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Firstly, you can think of finite potential well as a reasonable model instead of infinite potential well in order to visualize how electrons in are confined within the atom. So when it is excited with sufficient energies it can by principle escape the finite energy barriers of the well. Coming to the second part of your question which is "What do the free electrons do inside the metal "? The free electrons would be loosely bound to atoms and can become unbound even by receiving very low energies as compared to the more tightly bound electrons. This would lead to some transient motion until they lose some energy enough to be attracted by an atom again. And this whole process shall keep on repeating.

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