I'm trying to improve my conceptual understanding of Cooper pairs in a superconductor. Not how they come about such as discussed in this question, but more in the sense of what kind of picture I should have of the pair inside the SC itself.
The way I understand it is as follows: Cooper pairs are in fact bound states of two electrons. However, they are not bound states like we know them from molecules where the two guys are flying together all the time, like in an oxygen molecule. They are bound, but weakly bound. So I would suppose that for both electrons, if you follow them individually, they kind of fly around randomly. But if you study the correlations between them, you will see that there are non-zero correlations between them.
Is this an agreeable way of looking at them, or can someone offer an alternative/more refined/different picture? And how does one 'evolve' this picture of weakly-bound/correlated pairs into a single wavefunction with just a phase and an amplitude? Is that (as the above answer described) due to the fact that the pairs are (due to their weak binding) in general quite far away from each other, and thus their wavefunctions overlap with essentially all other pairs in the SC, forming the condensate?
I'm putting this in italics as it kind of distracts from the question, but does motivate my thought process a little. The reason I started thinking about this is motivated by Andreev bound states in SNS junctions (which result in the DC Josephson effect). To understand that one can think of an electron in the normal metal (N), which when incident upon the S part nucleates a Cooper pair in the S part while turning into a hole moving in the other direction in the N part. The hole then arrives at the other S part and destroys a Cooper pair there, before being reflected back as an electron again and repeating the process, leading to a supercurrent. Of course one can instead say that you have two pieces of superconductors with overlapping wavefunctions, resulting in the same physics. I understand that multiple pictures can be used to explain the same physics, but I'm trying to motivative how the two are connected.