Central Forces and Angular Momentum

Abstract

I have been dealing mainly with problems involving one dimensional motion. Since nature is three-dimensional, I want to look at solutions of Schrödinger’s equation in three dimensions. I consider only problems having spherical symmetry, that is, potentials that are a function of r only. These correspond to central forces. Moreover, for the most part, I restrict the discussion to bound state problems, such as the important problem of determining the bound states of the hydrogen atom. Problems related to continuum states will be discussed in the context of scattering theory in Chap. 18. Since angular momentum is conserved for central forces, we are led naturally to the quantum theory of angular momentum. It is important to remember, however, that the results to be derived for the angular momentum operator are valid independent of the specific nature of the interaction potential, spherically symmetric or not.