Open course ware

PROFESSOR: Our subject today then is Fermi's golden rule. So that's what we're going to develop. Fermi's golden rule. Fermi's golden rule. And this has to do with the study of transitions. And typically, the interesting and sophisticated thing about this subject is that you have a transition from some initial state to a state that is part of a continuum of states. That's what makes it complicated. The transition from one discrete state to another discrete state with a perturbation is kind of a simple matter to do. But when you can go into a continuum, you have to integrate over the set of final states, and that makes it a lot more interesting. So we go from a discrete state into a continuum. And that makes it somewhat challenging. So we will consider this in two forms. It's worth considering the case of what we call constant perturbations. And you might say, well, aren't we doing time dependent perturbation theory? Yes, we are. But this kin...

BARTON ZWIEBACH: Today's subject is momentum space. We're going to kind of discover the relevance of momentum space. We've been working with wave functions that tell you the probabilities for finding a particle in a given position and that's sometimes called coordinate space or position space representations of quantum mechanics, and we just talked about wave functions that tell you about probabilities to find a particle in a given position. But as we've been seeing with momentum, there's a very intimate relation between momentum and position, and today we're going to develop the ideas that lead you to think about momentum space in a way that is quite complimentary to coordinate space. Then we will be able to talk about expectation values of operators and we're going to be moved some steps into what is called interpretation of quantum mechanics. So operators have expectations values in quantum mechanism-- they are defined in a particular wa...