SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

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

- 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 
     - 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,

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