Matrix Elements of Symmetric Operators

Abstract

In this note we discuss an extension of a familiar theorem concerning the matrix elements of vector and tensor operators between states of definite angular momentum to the case of other groups than the full rotation group and to the case of operators of other symmetries. It is found that there is an extension to this theorem but in some cases there are nontrivial complications. In addition, a method is given for reducing a reducible representation of a group which gives explicitly the matrix elements in the appropriate similarity transformation.