Can two electrons be in the same state, when they belong to two different atoms, which are "far enough" (whatever that means) apart from each other? With "same state" I mean that (as far as specifiable) the states are really identical, except for the position of the electrons.
More specifically:
I am still not clear of how the separation of particles is taken into account for the Pauli exclusion principle. E.g. in a crystal the electrons seem close enough for the exclusion principle to become meaningful, for particles "a universe apart" from each other, it seems that it is kind of redundant (is there specific maths to that?), but what about everything in between?
(This is closely related to the talk Brian Cox gave, see this question: physics.stackexchange.com/q/18527/16689 )
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