# Pauli's exclusion principle and cooper pairs

Pauli exclusion principles states and I paraphrase; No two fermions can occupy the same state; That being said, how can cooper pairs exist? Cooper pairs are when two fermions(electrons in this case) bound together ; If they are bound together, then they must occupy the same state;

Staff Emeritus
If they are bound together, then they must occupy the same state;

That's your problem. They can be bound together without being in the same state. Atoms have electrons bound together (with a nucleus), and they are not in the same state.

Also, anticipating your next question, it's important to recognize that the PEP is a consequence of QM, not a fundamental principle. The fundamental principle is that for a collection of fermions, the wavefunction is antisymmetric under exchange of particles.

That's your problem. They can be bound together without being in the same state. Atoms have electrons bound together (with a nucleus), and they are not in the same state.

Also, anticipating your next question, it's important to recognize that the PEP is a consequence of QM, not a fundamental principle. The fundamental principle is that for a collection of fermions, the wavefunction is antisymmetric under exchange of particles.

you mean its not fundamental since it really applies only to fermions and not bosons; I don't quite understand how two electrons can be bound and not occupied the same state; They could occupy more than one states?

Staff Emeritus
By "not fundamental" I mean it's a derived property of something that is more fundamental. The fundamental property is the wavefunction symmetry.

As far as binding - the earth has zillions of electrons gravitationally bound to it. Do you think they are all in the same state?

If they are bound together, then they must occupy the same state;

What's your reasoning behind that statement? Or at least where did you see it? With context we should be able to show you why that is not true for Cooper pairs.

f95toli
Gold Member
The electrons in a Cooper pair have opposite spins (+1/2 and -1/2), that alone should be enough to convince you that they are not in the same state.

Staff Emeritus