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PROFESSOR: We're talking about angular momentum. We've motivated angular momentum as a set of operators that provided observables, things we can measure. Therefore, they are important. But they're particularly important for systems in which you have central potentials. Potentials that depend just on the magnitude of the radial variable. A v of r that depends just on the magnitude of the vector r relevant to cases where you have two bodies interacting through a potential that just depends on the distance between the particles. So what did we develop? Well, we discussed the definition of the angular momentum operator. You saw they were Hermitian. We found that they satisfy a series of commutators in which lx with ly gave ih bar lz, and cyclical versions of that equation, which ensure that actually you can measure simultaneously the three components of angular momentum. You can measure, in fact, just one. Happily we found there was another object we could measure...

PROFESSOR: So angular momentum, we need to deal with angular momentum, and the inspiration for it is classical. We have L is r cross p. Classically. So let's try to just use that information and write the various operators. And in fact, we're lucky in this case. The operators that we would write inspired by the classical definition are good operators and will do the job. So what do we have? Lx, if you remember the cross-product rule, that would be y Pz minus z Py. Now you can think of this thing as a cyclic, like a circle when you have x and Px, y and Py, and z and Pz. Things are cyclically symmetric. There's no real difference between this core. And so you can go cyclically here. So you say, let's go cyclical on this index. Ly is equal to the next cyclic to y in that direction is z Px minus x Pz. And Lz is equal to x Py minus y Px. And these things, I'll think of them as the operators. Let's put hats to everything. The first thing I can wonder wit...