L17.3 Properties of Berry's phase
PROFESSOR: So my comments. First one-- if the psi n of t can be chosen to be real, the geometric face vanishes. So why is that? The geometric face is, remember, the integral of this new factor, which was i psi n of t psi n of t dot. You had to integrate that thing to get the geometric face. We explained that this quantity in general is-- well, in general, it's always imaginary, this quantity. And then with an i, this is a real quantity which we've been using. But if this is imaginary-- look at this. This is imaginary. How can it be imaginary if psi is real? It can't be. If psi is real, imagine doing that integral. You can kind of imagine. So it has to be 0 if psi is real. Yes? AUDIENCE: [INAUDIBLE]. Why did we say that was imaginary? PROFESSOR: We proved this was imaginary. We did calculate the derivative with respect to time of psi with psi, and we proved that this was imaginary. And now I'm saying if this was imaginary but if psi is real, the only possib...