The analytical Scheme calculator for angular momentum coupling and recoupling coefficients

Abstract

We describe a Scheme implementation of the interactive environment to calculate analytically the Clebsch–Gordan coefficients, Wigner 6 j and 9 j symbols, and general recoupling coefficients that are used in the quantum theory of angular momentum. The orthogonality conditions for considered coefficients are implemented. The program provides a fast and exact calculation of the coefficients for large values of quantum angular momenta. Program summary Title of program:Scheme2Clebsch Catalogue number:ADWC Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWC Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed:Any Scheme-capable platform Operating systems under which the program has been tested: Windows 2000 Programming language used:Scheme Memory required to execute with typical data:50 MB (≈ size of DrScheme, version 204) No. of lines in distributed program, including test data, etc.: 2872 No. of bytes in distributed program, including test data, etc.: 109 396 Distribution format:tar.gz Nature of physical problem:The accurate and fast calculation of the angular momentum coupling and recoupling coefficients is required in various branches of quantum many-particle physics. The presented code provides a fast and exact calculation of the angular momentum coupling and recoupling coefficients for large values of quantum angular momenta and is based on the GNU Library General Public License PLT software http://www.plt-scheme.org/. Method of solution:A direct evaluation of sum formulas. A general angular momentum recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta is expressed as a sum over products of the Clebsch–Gordan coefficients. Restrictions on the complexity of the problem:Limited only by the DrScheme implementation used to run the program. No limitation inherent in the code. Typical running time:The Clebsch–Gordan coefficients, Wigner 6 j and 9 j symbols, and general recoupling coefficients with small angular momenta are computed almost instantaneously. The running time for large-scale calculations depends strongly on the number and magnitude of arguments' values (i.e., of the angular momenta).