Pauli's exclusion principle and cooper pairs

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Discussion Overview

The discussion centers around the Pauli exclusion principle (PEP) and its implications for the existence of Cooper pairs, specifically addressing how two fermions, such as electrons, can be bound together while adhering to the PEP. The scope includes theoretical considerations and conceptual clarifications related to quantum mechanics and superconductivity.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants assert that if two fermions are bound together, they must occupy the same state, questioning the existence of Cooper pairs under the PEP.
  • Others argue that fermions can be bound without occupying the same state, citing examples such as electrons in atoms that are bound to a nucleus.
  • It is noted that the PEP is a consequence of quantum mechanics (QM) and that the fundamental principle involves the antisymmetry of the wavefunction for fermions.
  • One participant raises a question about the existence of P-wave superconductors, suggesting that the example of Cooper pairs may not be the best illustration for the argument being made.
  • Another participant mentions that Cooper pairs consist of electrons with opposite spins, indicating that they are not in the same state.
  • There is a reference to strontium ruthenates as a material thought to exhibit spin-triplet pairing, which may relate to the broader discussion of Cooper pairs.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the implications of the PEP for Cooper pairs, and there is no consensus on the interpretation of how fermions can be bound without occupying the same state.

Contextual Notes

Participants express uncertainty about the definitions and implications of the PEP and wavefunction symmetry, and there are unresolved questions regarding the nature of binding and state occupancy in the context of Cooper pairs.

noblegas
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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;
 
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noblegas said:
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.
 
Vanadium 50 said:
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?
 
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?
 
noblegas said:
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.
 
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.
 
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.
 
I believe strontium ruthenates are thought to have spin-triplet pairing.

Zz.
 

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