Point Group Symmetry Applications: Methods and Tables

✍ Scribed by Philip H. Butler (auth.)

• Publisher: Springer US
• Year: 1981
• Tongue: English
• Leaves: 563
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-6
Basic Concepts....Pages 7-41
The jm Factors and j Symbols....Pages 43-81
The Wigner— Eckart Theorem....Pages 83-97
O 3 and Its Subgroups....Pages 99-127
Properties of the Dihedral Groups....Pages 129-137
Fractional Parentage Coefficients....Pages 139-151
Time Reversal....Pages 153-169
Applications....Pages 171-186
Programming Notes....Pages 187-188
Group Information Tables....Pages 189-206
Branching Rule Tables....Pages 207-216
jm Factor Tables....Pages 217-427
3 j and 6 j Symbol Tables....Pages 429-461
9 j Symbols....Pages 463-511
Bases in Terms of Spherical Harmonics....Pages 513-551
Back Matter....Pages 553-567

✦ Subjects

Mechanical Engineering