# Superconductivity and Pauli exclusion principle

1. Jul 8, 2010

### haael

I have the following problem understanding Pauli exclusion principle.

Two identical fermions can't share the same quantum state. Two bosons can.
Now Cooper pairs are bosons made up from fermions. Everything clear up to this point.
Now several Cooper pairs can share the same quantum state, since they are bosons.

And now: how do electrons inside particular Cooper pairs consider them different?

I mean: if every Cooper pair is identical to any other and all of them are in the same quantum state, then every such Cooper pair is the same quantum state.

How do electrons know they belong to different Cooper pairs when all of them are the same?

I bet the interactions inside a pair have something to do with it. But how it is mathematically described? How come electrons can tell apart different pairs from inside and still each of them looks the same from outside?

My questions also extend to superfluids and all bosons composed of fermions that share the same quantum state.

2. Jul 8, 2010

### Ben Niehoff

Cooper pairs are very large, on the order of hundreds of atoms in diameter. This is what allows two Cooper pairs to effectively share states. In reality, two overlapping Cooper pairs cannot share exactly the same state, because the pairs are composed of fermions that obey Pauli exclusion. However, since the Cooper pairs are so large, very minute differences in quantum state can be effectively ignored, and so they behave more or less like bosons. Cooper pairs do not exactly follow a Bose-Einstein distribution, but they come quite close (and can be made arbitrarily close under appropriate conditions).

3. Jul 9, 2010

### haael

Wait, does that mean that there are no true composite bosons and only elementary particles can have Bose-Einstein statistics?

4. Jul 9, 2010

### ZapperZ

Staff Emeritus
The problem here is two-fold.

1. Remember that via the indistinguishably concept, you can't really track which electron does what.

Zz.