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This is the Pauli Exclusion Principle, but I have a question about it... It states that no two identical fermions can have the same quantum state, but what about different fermions having the same quantum state?

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    $\begingroup$ What does "different" mean? $\endgroup$ – WillO Aug 8 '15 at 20:21
  • $\begingroup$ If by different you mean different spatial part of the wavefunction, then they can have the same "quantum state", if by this you mean the spin component of the wavefunction. What can't really happen is to have two identical electrons in the same quantum state, in the sense that they cannot have the wavefunction (i.e. spatial and spinor part) as a consequence of the anticommutation relations. $\endgroup$ – Phoenix87 Aug 8 '15 at 21:27
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    $\begingroup$ By "different", do you mean, for example, an electron and a muon? In that case, there is no restriction to their states. $\endgroup$ – Bosoneando Aug 8 '15 at 21:37
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    $\begingroup$ @JakeLebovic that's a contraction in terms. $\endgroup$ – DanielSank Aug 8 '15 at 22:10
  • $\begingroup$ Can two non identical particles ever be in the same state? $\endgroup$ – Apoorv Khurasia Aug 9 '15 at 1:48
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A muon and a positron are different species so the wavefunction need not be symmetric or antisymmetric under interchange of the positions of the two different particles.

That's good since the momentum operator takes the derivative in that particles direction and then scales by that particles mass, so it would be weird if they swapped.

So you can have an infinite square well, have both in the ground state and have them both be spin up. Of course that assumes they don't interact, but an interaction won't make their wavefunction antisymmetric it will just give them a potential between the two.

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