The intelligent states. I. Group-theoretic study and the computation of matrix elements

In this first of a series of papers, a group-theoretic study is presented of the quasi-intelligent states which are a generalization of the intelligent states satisfying equality in the Heisenberg uncertainty relation ΔJ12ΔJ22? (1/4) ‖〈J3〉‖2. A method based on the knowledge of a certain generating function is given for the calculation of matrix elements of polynomials in the infinitesimal generators of the rotation group between quasi-intelligent states. Examples of such computations are also included to exhibit the improvement and efficiency of the present methods.