Levinson's theorem, part 1
PROFESSOR: Levinson's theorem, in terms of derivations, that we do in this course, this is probably the most subtle derivation of the semester. It's not difficult, but it's kind of interesting and a little subtle. And it's curious, because it relates to things that seem to be fairly unrelated. But the key thing that one has to do is you have to use something. How all of the sudden are you going to relate phase shifts to bound states? The one thing you have to imagine is that if you have a potential and you have states of a potential, if the potential changes, the states change. But here comes something very nice. They never appear or disappear. And this is something probably you haven't thought about this all that much. Because you had, for example, a square, finite square well. If you made this more deep, you've got more bound states. If you made it less deep, the bound states disappear. What does it mean the bound states disappear? Nothing, reall...