The Nature of the Cooper Pair - University of Liverpool

We apply the relation
Multiply
� R
0 sin(kr) sin(k′ r)dr =
�
k ′
�
�2k ′2
ak ′
me
− E
by sin(kr) and integrate, we get
where
R
2 a k
�
� � 2 k 2
me
�
R/2 for k = k ′
0 otherwise
sin(k ′ r) = −V (r) �
ak ′ sin(k ′ r)
− E
� l
�
k ′
= − �
ak ′Vkk ′,
Vkk ′ = V0
0 sin(kr) sin(k′ r)dr.
The upper limit is l instead of R because V (r) is zero for r > l.
Superconductivity 37
k ′