Abstract:

Quantum theory of angular momentum provides an invaluable tool for all quantum mechanical phenomena, occuring in the fields of atomic, molecular, and nuclear physics. The symmetries of Angular Momentum coupling and Angular momentum recoupling coefficients are viewed in terms of sets of hypergeometric functions of unit argument and their polynomial or nontrivial zeros are studied. A fundamental theorem dealing with the minimum number of parameters necessary and sufficient to obtain the complete set of solutions for multiplicative diophantine equations of degree n is stated and proved. The complete set of solutions for the polynomial zeros of degree 1 of the 6j coefficient is targetted and related to the solutions of the homogeneous multiplicative diophantine equation of degree 3; Raising factorial, lowering factorial formal binomial expansions are obtained. Triple sum series is evaluated as a folded triple sum. The identification of the triple sum series with a triple hypergeometric series in chapter 5 enables for the first time the study of polynomial or nontrivial zeros for the 9j coefficient. The conventional single sum over the product of three 6j coefficients will not reveal these polynomial zeros. 