Construction of Orthonormal Angular-Momentum Operators

Abstract

The problem of constructing an orthonormal basis for the (2j + 1)2-dimensional space of angular-momentum operators is reduced to the problem of constructing a sequence of orthogonal polynomials of a discrete real variable. A number of properties of the polynomials are obtained, including a pure recurrence formula and several mixed recurrence relations. Three explicit representations of the polynomials are given, together with a table of orthonormal angular-momentum operators.