Energy below the barrier and phase shift
PROFESSOR: Let's do E less than V not. So we're back here. And now of the energy e here is v not is x equal 0. X-axis. And that's the situation. Now you could solve this again. And do your calculations once more. But we can do this in an easier way by trusting the principle of analytic continuation. In this case, it's very clear and very unambiguous. So the big words, analytic continuation, don't carry all the mathematical depth. But it's a nice, simple thing. We first say that the solution is the same for x less than 0. So for x less than 0, we write the same solution. Because the energy is greater than 0, or all what we said here, the value of k squared, a into the ikhd e to the minus i k x. It's all good. And k squared is still 2 m e over h squared. The problem is the region where x is greater than 0. Because there you have an exponential. But now you must have a decaying exponential. But we know how that should work. It should really be an ...