If a crystal is a quantum system, what are its quantum numbers? You will see there are many, really many quantum numbers needed. Hence, we will discuss various ways to condense this information into a manageable form.
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When the lattice parameter of fcc-Al grows to infinity, the Al-atoms will eventually not feel each other any longer. They have become free atoms. Therefore, we should recover the same energy levels as for a free atom. You band structure will be a set of flat horizontal lines, positioned at the same energies as the energy levels in a free Al atom.
In this way, you see how there is a continuous transition from the mental picture of orbitals (and their energies) in a free atom, to orbitals (and their energies) in a crystal.
Refering to the end of the video: explain why the four band structure pictures evolve as they do, and tell how the picture would look like (and why) in the limiting case of an infinitely large lattice parameter.
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