The Nature of the Cooper Pair - University of Liverpool

So we have found a bound pair - a wavefunction of two
electrons that has a finite size. This is in spite of the fact that
the kinetic energies of the electrons, which are close to E F , are
much larger than the binding energy ∆.
Mathematically, we have seen that this solution is obtained
after we impose the condition that the wavefunction sum
Ψ = � α k sin kr
must not contain any wavevector below that Fermi level.
We can interpret this physically. If the bound pair of electrons
separate, they become plane waves and would have to occupy
two of the energy states below E F . However, we are talking
about 0 K, and all states below E F are fully. There is no room
for any more electron, because of the exclusion principle. That
is why the pair must, with an energy just below E F (by ∆),
must remain bound.
Superconductivity 25