As i understand it, the commutation rules for the quantum angular momentum operator in x, y, and z (e.g. Lz = x dy - ydx and all cyclic permutations) are the same as the lie algebras for O3 and SU2. I'm not entirely clear on what the implications of this are. So I can think of Lz as generating physical rotations of the wavefunction? Why is that important? I suspect, if we're working in a spherically symmetric potential, that this has something to do with eigenvalues and ladder functions. But the connections are very murky to me still. Can anyone explain? Or point me to some notes that get to the punchlines really fast? I don't care about proofs so much. This is all super confusing cause I'm teaching myself all this. I have a *basic* understanding of group theory (level: Artin) and of QM (level: high Griffiths/low Shankar).