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Point Group Symmetry Applications

Methods and Tables

  • Book
  • © 1981

Overview

Authors:
  1. Philip H. Butler

    1. University of Canterbury, Christchurch, New Zealand

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Philip H. Butler
    Pages 1-6

  3. Basic Concepts

    • Philip H. Butler
    Pages 7-41

  4. The jm Factors and j Symbols

    • Philip H. Butler
    Pages 43-81

  5. The Wigner— Eckart Theorem

    • Philip H. Butler
    Pages 83-97

  6. O3 and Its Subgroups

    • Philip H. Butler
    Pages 99-127

  7. Properties of the Dihedral Groups

    • Philip H. Butler
    Pages 129-137

  8. Fractional Parentage Coefficients

    • Philip H. Butler
    Pages 139-151

  9. Time Reversal

    • Philip H. Butler
    Pages 153-169

  10. Applications

    • Philip H. Butler
    Pages 171-186

  11. Programming Notes

    • Philip H. Butler
    Pages 187-188

  12. Group Information Tables

    • Philip H. Butler
    Pages 189-206

  13. Branching Rule Tables

    • Philip H. Butler
    Pages 207-216

  14. jm Factor Tables

    • Philip H. Butler
    Pages 217-427

  15. 3j and 6j Symbol Tables

    • Philip H. Butler
    Pages 429-461

  16. 9j Symbols

    • Philip H. Butler
    Pages 463-511

  17. Bases in Terms of Spherical Harmonics

    • Philip H. Butler
    Pages 513-551

  18. Back Matter

    Pages 553-567
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Keywords

About this book

The mathematical apparatus of group theory is a means of exploring and exploiting physical and algebraic structure in physical and chemical prob­ lems. The existence of structure in the physical processes leads to structure in the solutions. For group theory to be useful this structure need not be an exact symmetry, although as examples of exact symmetries we have that the identity of electrons leads to permutation symmetries in many-electron wave functions, the spatial structure of crystals leads to the Bloch theory of crystal eigenfunctions, and the rotational invariance of the hydrogenic Hamiltonian leads to its factorization into angular and radial parts. In the 1930's Wigner extended what is known to mathematicians as the theory of group representations and the theory of group algebras to study the coupling coefficients of angular momentum, relating various properties of the coefficients to the properties of the abstract group of rotations in 3-space. In 1949 Racah, in a paper on rare earth spectra, showed that similar coefficients occur in other situations. Immediately a number of studies of the coefficients were begun, notably by Jahn, with his applications in nuclear physics. In the years since then a large number of physicists and chemists have added to the development of a general theory of the coefficients, or have produced specialized tables for a specific application. Applications now range from high-energy physics to biology.

Authors and Affiliations

  • University of Canterbury, Christchurch, New Zealand

    Philip H. Butler

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