We know that two particles can't exist in identical quantum states in the same place, fair enough. However, no particle can be sitting directly on top of another to infinite precision. Therefore, you can always say they're some minimum distance away from one another. Now suppose you have two atoms sitting in a crystal lattice next to one another. One has its electrons sitting around doing their thing, and so does another, so they're to all intents and purposes identical. Identical. Isn't this forbidden? The two atoms have electrons sitting in the same quantum states in their electron clouds. They're some small distance away from one another as before, so what's changed? What's fundamentally different about the distance between two electrons in one atom's electron cloud - which forbids identical quantum states - and the distance between electrons in neighbouring clouds?