ABSTRACT
Index notation is the modern and easy way to work through problems such as we now face. In this chapter, the authors define an angular momentum by a set of three operators and use the Einstein summation convention. This simply means that an index repeated once is summed over, as distinct from those appearing once, which is a free one for the readers to pick. The same index appearing three or more times is an error. The readers can always use Casimirs as part of their complete commuting set of observables. The coefficient of the square root is real and positive by phase convention.
