O(3) shift operators: The general analysis

Abstract

O(3) shift operators are constructed in terms of tensor operators T (j,μ) and the O(3) generators. These are of type Bkl, k=−j,...,j, where Bkl raises l by k, l (l+1) being the eigenvalue of the O(3) Casimir operator. Various convenient normalizations of these operators are constructed, and their properties and uses considered.