Pauli's exclusion principle and cooper pairs

[noblegas]

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;

 

[Vanadium 50]

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.

 

[noblegas]

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?

 

[Vanadium 50]

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?

 

[Tingish]

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]

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.

 

[Vanadium 50]

Is that true? Are there P-wave superconductors? (In analogy with 3He superfluidity) I'm not arguing that Cooper pairs are in the same state - just that this might not be the best example.

 

[ZapperZ]

I believe strontium ruthenates are thought to have spin-triplet pairing.

Zz.