Simultaneous eigenstates and quantization of angular momentum
PROFESSOR: Simultaneous eigenstates. So let's begin with that. We decided that we could pick 1 l and l squared, and they would commute. And we could try to find functions that are eigenstates of both. So if we have functions that are eigenstates of those, we'll try to expand in terms of those functions. And all this operator will become a number acting on those functions. And that's why the Laplacian simplifies, and that's why we'll be able to reduce the Schrodinger equation to a radial equation. This is the goal. Schrodinger equation has r theta and phi. But theta and phi will deal with all the angular dependents. We'll find functions for which that operator gives a number acting on them. And therefore, the whole differential equation will simplify. So simultaneous eigenstates, and given the simplicity of l z, everybody chooses l z. So we should find simultaneous eigenstates of this two things. And let's call them psi l m of theta and phi. Whe...