  The Cooper pair is generally analyzed in momentum space, but its real-space
structure also follows directly from the BCS theory. It is shown here that this
leads to a spherically symmetrical quasi-atomic wavefunction, with an identical
"onion-like" layered structure for each of the electrons constituting the
Cooper pair, with charge layers ~ 0.1 nm and a radius ~ 100 nm for a classic
BCS superconductor. This charge modulation induces a corresponding charge
modulation in the background ionic lattice, and the attractive interaction
between these two opposite charge modulations produces the binding energy of
the Cooper pair. This physically-based interaction potential is similar to that
in the simple BCS approximation. The implications of this real-space picture
for understanding conventional and exotic superconductors are discussed.
