L20.5 Identification of phase shifts. Example hard sphere
PROFESSOR: I want to demonstrate two ways in which you can see phase shift. So basically, the reason we use phase shift is that these are the things that you can calculate. Calculating phase shifts is possible. So how do you do that? We'll be a two-step procedure. We'll only finish that next time. But let's get started. So suppose you have your wave again. And for a fixed l, a given partial wave, this is the full solution for this scattering problem. It is an Al Jl of kr plus bl at Nl of kr. y l0. That's your solution. The signal that you got scattering, and you have something right here, is the existence of this term, because when there's no potential and no scattering, the solution is valid all the way to r equals 0, and therefore, this has no singularity. But this term is saying that this solution doesn't extend all the way to r equals 0, because this diverges. So something un-trivial is happening. So bl is the signal that they're scattering...