Rotation and Angular Momentum

There is a fundamental connection between the angular momentum (a mechanical quantity) and the rotation operators (which is a symmetry group). The angular momentum is the generator of rotations. Because of this connection, many properties of angular momentum operators can be derived from the properties of the rotation group. We will derive these properties (mainly the commutation relations) starting only from this fact. In this way we will be able to deal not only with the orbital angular momentum but also with all the other kinds of angular momenta, like the intrinsic angular momentum of particles called spin. In the following section, we will concentrate mainly on the rotations themselves. After that, we will apply these to quantum mechanical systems.