Effects of resonance on phase shifts, wave amplitude and time delay
PROFESSOR: This is the answer. Tan of 2 k a plus delta. It's a little messy, no wonder. Just plotted this functions. [INAUDIBLE] Sin k plus a cosh kappa a [INAUDIBLE] plus a prime over kappa cosh a prime a sinh kappa a. You have sin a prime a sinh. The sinh causes outer [INAUDIBLE] the same but this one changes. Centered here, k prime over kappa cos k prime a cosh kappa a. So it's a well-defined expression, if you know the number of kappa a, you can calculate everything. Let me just make sure you can see that. If you know-- if you said, for example, ka, this is a natural variable. ka is just-- the k is related to the energy direction. So ka has no limits, call it u. Then you have two parameters of the square well [INAUDIBLE],, a depth we don't and a height we want. So there's natural to define just [INAUDIBLE] would have z 0 squared which is 2m v 0 a squared over h squared. You also define z 1 squared [INAUDIBLE] as 2m v1 a squared over h squared. And then...