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Point Group Symmetry Applications - Methods and Tables (Paperback, Softcover reprint of the original 1st ed. 1981)
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Point Group Symmetry Applications - Methods and Tables (Paperback, Softcover reprint of the original 1st ed. 1981)
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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.
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