# Spherical Coordinates

### From FSUPhysicsWiki

We now write down the Cartesian components of the angular momentum operator in spherical coordinates. We will make use of this result later in determining the eigenfunctions of the angular momentum squared and of one of its components.

The Cartesian coordinates and can be written in terms of the spherical coordinates and as follows:

Let us start with the component of the angular momentum, In Cartesian coordinates, this is

If we make use of the chain rule, then we obtain

Similarly, the and components may be found to be

and

## Problem

(Richard L. Liboff, *Introductory Quantum Mechanics*, 2nd Edition, pp. 377-379)

Show, using the above results, that the operator,

when applied to a function of the azimuthal angle rotates the angle to That is, show that