Matrix Representation of the Angular Momentum Projection Operator

Abstract

Formulas are obtained which give the matrix representation, relative to a product basis, of the projection operator for the total angular momentum of a system. If the individual angular momenta are not too large, the matrix elements depend upon a small number of parameters, independent of the number of angular momenta coupled. Recurrence relations between elements and symmetry properties of elements are derived. These results enable one to perform the vector coupling of a large number of angular momenta in a relatively simple fashion. The connection between the matrix elements and vector coupling coefficients is discussed. Several important special cases are treated in detail.