Angular Momentum in Quantum Mechanics

We begin with a review of the basic concepts involved in the quantum mechanical description of physical systems and the notation we will use in the lectures. The notes in this Section are not intended to provide an introductory course on Quantum Mechanics. They assume the reader has had at least a first course at undergraduate physics level that covers some historical background and reviews the experimental evidence that leads to the necessity for the formalism developed here as the most useful description we have of nature at the subatomic level. Some familiarity with matrices, differential equations, complex numbers and vector is assumed. The basic concepts of Dirac’s vector space formulation of non-relativistic Quantum Mechanics are described in an informal, non-rigorous way. We believe that this formalism provides the best and most economical framework for understanding of the quantum world in a notation that is of great practicality for the description of many-body systems. We believe that these advantages outweigh any difficulties that may arise because of the abstractions involved. These difficulties are no worse then those involved in mastering the concept of vectors in physical space.