ABSTRACT
Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. The product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. These considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.
