# Angular Momentum

### From FSUPhysicsWiki

In this chapter, we will discuss the treatment of angular momentum in quantum mechanics. The quantization of angular momentum was first observed in the Stern-Gerlach experiment in 1922 through the deflection of silver atoms passing through a spatially inhomogeneous magnetic field. We will show how this quantization is formulated mathematically within the framework of modern quantum mechanics, as opposed to the old quantum theory that the Stern-Gerlach experiment was intended to test.

We will derive the commutation relations satisfied by the components of the angular momentum operator and show that only the magnitude and one component of the angular momentum may be determined exactly. Both will turn out to be quantized. We also show that angular momentum acts as a generator of rotations, similarly to how linear momentum generates translations. Finally, we find the common eigenfunctions of the magnitude of the orbital angular momentum squared and of one of its components, which are the spherical harmonics.