A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)
The graphic technique of Kuznetsov-Smorodinov for the SUq(2) quantum algebra is discussed. The transformation of trees including the braiding of branches is considered. Using the universal R-matrix the q-analog of 9j-symbol is introduced and its symmetry are examined
Formulas for Clebsch-Gordan Coefficients, 6-j symbols and 9-j symbols of SU(2) are presented in a ready-to-program way for obtaining algebraic tables. An excerpt of the complete tables are also presented. (Author)
In this study, Clebsch-Gordan coefficients, 3j symbols, Racah coefficients, Wigner's 6j and 9j symbols were calculated by a prepared computer code of COEFF. The computer program COEFF is described which calculates angular momentum coupling coefficients and expresses them as quotient of two integers multiplied by the square root of the quotient of two integers. The program includes subroutines to encode an integer into its prime factors, to decode of prime factors back into an integer , to perform basic arithmetic operations on prime-coded numbers, as well as subroutines which calculate the coupling coefficients themselves. The computer code COEFF had been prepared to run on a VAX. In this study we rearranged the code to run on PC and tested it successfully. The obtained values in this study, were compared with the values of other computer programmes. A pretty good agreement is obtained between our prepared computer code and other computer programmes
Spin networks, namely, the 3nj symbols of quantum angular momentum theory and their generalizations to groups other than SU(2) and to quantum groups, permeate many areas of pure and applied science. The issues of their computation and characterization for large values of their entries are a challenge for diverse fields, such as spectroscopy and quantum chemistry, molecular and condensed matter physics, quantum computing, and the geometry of space time. Here we record progress both in their efficient calculation and in the study of the large j asymptotics. For the 9j symbol, a prototypical entangled network, we present and extensively check numerically formulas that illustrate the passage to the semiclassical limit, manifesting both the occurrence of disentangling and the discrete-continuum transition.