Spin Operators and Commutation in Quantum Physics

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 L_x, L_y, and L_z, are these commutation relations:

All the orbital angular momentum operators, such as L_x, L_y, and L_z, have analogous spin operators: S_x, S_y, and S_z. And the commutation relations work the same way for spin: