Products of Angular Momentum Matrices and Their Traces

A. Bose

Gordon Leslie Squires

P. R. Subramanian, Varadarajan Devanathan

General expressions for traces of products of angular momentum matrices (both in Cartesian and spherical bases) for systems of arbitrary spin are derived using the well established properties. It is shown that the trace is a polynominal in eta where eta is the eigenvalue of the J 2 operator. The trace techniques developed herein are applied to the problems of spin orientation.

Naeem Ullah

The products of exponentials containing various angular momentum operators are expressed on a single rotation operator. This gives new expressions for the traces of products of angular momentum operators in terms of hypergeometric functions. Since hypergeometric functions are related to Jacobi polynomials, the traces can also be expressed in terms of these polynomials.