Pauli's exclusion principle and cooper pairs

In summary, the conversation discusses the Pauli exclusion principle and its application to Cooper pairs. The participants also touch on the fundamental nature of the principle and its relationship to quantum mechanics. Finally, they discuss the possibility of Cooper pairs occupying different states and provide examples of this phenomenon in other systems.
  • #1
noblegas
268
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
I believe strontium ruthenates are thought to have spin-triplet pairing.

Zz.
 

Related to Pauli's exclusion principle and cooper pairs

What is Pauli's exclusion principle and how does it relate to cooper pairs?

Pauli's exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can exist in the same quantum state simultaneously. This principle is closely related to the formation of cooper pairs, which are pairs of electrons that have opposite spin and therefore do not violate the exclusion principle.

How does Pauli's exclusion principle contribute to superconductivity?

In superconductors, cooper pairs form at very low temperatures due to the interaction of electrons with the crystal lattice. These pairs are able to flow through the material without resistance, which is a phenomenon that cannot be explained without the exclusion principle. Without the exclusion principle, electrons would not be able to form these pairs and superconductivity would not occur.

What is the significance of cooper pairs in superconductivity?

Cooper pairs are crucial in understanding and explaining superconductivity. They allow for the phenomenon of superconductivity to occur at low temperatures, where electrons are able to flow through the material without resistance. This has important practical applications, such as in the development of more efficient electrical transmission systems.

Can cooper pairs exist in materials other than superconductors?

Although cooper pairs are most commonly associated with superconductivity, they can also exist in other materials. For example, in certain systems, such as liquid helium, cooper pairs can form and exhibit similar behavior to superconductors, even at higher temperatures.

How does the formation of cooper pairs impact the properties of the material?

The formation of cooper pairs has a significant impact on the properties of a material. In superconductors, it allows for the material to have zero electrical resistance and expel magnetic fields, making it useful for a variety of applications. In other materials, the formation of cooper pairs can also lead to changes in conductivity, thermal properties, and other physical properties.

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