In many introductions to the pauli's exclusion principle, it only said that two identical fermions cannot be in the same quantum state, but it seems that there is no explanation of the range of those two fermions. What is the scope of application of the principle of exclusion? Can it be all electrons in an atom, or can it be electrons in a whole conductor, or can it be a larger range?
[Physics] the range of Pauli’s exclusion principle？
fermionsidentical-particlespauli-exclusion-principlequantum mechanics
Best Answer
All electrons (and all elementary particles) in the universe are supposed to have exactly identical properties according to the standard model. This means that for electrons, the Pauli exclusion principle reads "No 2 electrons in the universe can occupy the same state".
But due to the phrasing of your question, I think you might also have a wrong idea of what exactly constitutes a "same state". For instance, if you have two atoms of hydrogen 1 km apart, both could have an electron in the "same" $1s$ state. This is simply because these two states are different. While they are both $1s$ states, they are associated with different atoms.
In a crystal, the picture is slightly different because strictly speaking the eigenstates are Bloch states which are delocalized over the while crystal. But for the deepest levels (the ones well below the conduction level), the picture of localized states localized around each atom is not so off. In that case, all atoms in the crystal will typically have these states occupied, but again this is not in opposition with Pauli's principle because the states are distinguishable due to being associated with different atoms.