Don’t think quantum physics is devoid of anything but dry science. The fact is that it’s full of relationships, they’re just commutation relationships — which are pretty dry science after all. In any case, among the angular momentum operators Lx, Ly, and Lz, are these commutation relations:


All the orbital angular momentum operators, such as Lx, Ly, and Lz, have analogous spin operators: Sx, Sy, and Sz. And the commutation relations work the same way for spin: