Topic #13 --------------- OP-SF NET ---------------- November 15, 1996 ~~~~~~~~~ From: K. Srinivasa Rao Subject: book announcement on Quantum Theory of Angular Momentum The following book may be of interest to some of you: "Quantum Theory of Angular Momentum: Selected Topics" by K. Srinivasa Rao and V. Rajeswari, published by Springer-Verlag and Narosa Publishing House (1993). The topics selected for study in this 315-page research monograph are: - Connection between the angular momentum coupling (3-j) and recoupling (6-j and 9-j) coefficients and generalized hypergeometric functions of unit argument. - Transformation theory of generalized hypergeometric functions and the relation of the different 3-j coefficient forms (due to Van der Waerden, Wigner, Racah, Majumdar, Raynal). - Relation between the 3-j coefficient and the Hahn polynomial, the 6-j coefficient and the Racah polynomial and their consequences for recurrence relations. - Polynomial (or non-trivial) zeros of angular momentum coefficients: - closed form, formal binomial expansions for the 3-j, 6-j and 9-j coefficients. - Degree 1 zeros and multiplicative Diophantine equations. - Polynomial zeros of higher degrees. - Polynomial zeros and exceptional Lie algebras. - Numerical algorithms for the generation of polynomial zeros. - q-3-j and q-6-j coefficients and their relation to sets of basic hypergeometric series. - Numerical computation of angular momentum coefficient : - The 3-j coefficient, using the set of six 3F2(1)'s. - The 6-j coefficient, using two sets of three and four 4F3(1)'s. - The 9-j coefficient, using the triple sum series. - Parallel computation of the 9-j coefficient, using the hierarchic formulae. Fortran programs for the computation of the 3-j, 6-j and 9-j coefficients are included for use by atomic, molecular and nuclear Physicists / Chemists. This research monograph builds on the standard text book material contained in, for example: A.R. Edmonds (1957), Angular Momentum in Quantum Physics, Princeton Univ. Press. and it leads the reader to the recent developments in the selected topics. The contents of this book supplement the results in L.C. Biedenharn and J.D. Louck, "Angular Momentum in Quantum Physics" and "Racah-Wigner Algebra in Quantum Physics", Encyclopaedia of Mathematics and its Applications, Vols. 8 and 9. and the compilation of all the known formulae in this field contained in the book : D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific (1988) (English edition of the original Russian publication Nauka, Leningrad, 1975).