The Nature of the Cooper Pair - University of Liverpool

If V (r) is constant, the solution is of the form
ψ(r) = sin(kr).
However, V (r) is not constant. It becomes zero beyond r = l.
We can try a sum of sine functions:
Ψ(r) = �
ak sin(kr),
where a k are unknown constants that we must find.
k
We now come the the important part. The need for this sum
means that energy states with many wavevectors k must be
used to make up the wavefunction. However, we are not
allowed to use k values below the Fermi energy, because those
states are fully occupied.
Therefore, we must impose the condition that k must be more
than k F , the wavevector at the Fermi energy.
The detailed steps to solve the Schrodinger equation are given
in the appendix.
Superconductivity 19