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.