Free Ebook Point Group Symmetry Applications: Methods and Tables, by Philip H. Butler
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Point Group Symmetry Applications: Methods and Tables, by Philip H. Butler
Free Ebook Point Group Symmetry Applications: Methods and Tables, by Philip H. Butler
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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.
- Sales Rank: #7344793 in Books
- Published on: 1981-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x 1.32" w x 5.98" l, 1.69 pounds
- Binding: Paperback
- 576 pages
Most helpful customer reviews
2 of 2 people found the following review helpful.
Comprehensive and Useful Guide
By William Kirk
This is a treatment of Group Theory applications to problems in quantum chemistry and physics, especially spectroscopy, although as the author points out very early, there is no reason to limit the applications to spectroscopy. This book has been an invaluable aid in my research, it is concise, and well-thought out. A good understanding of linear algebra is required, and it would be helpful to have some prior aquaintance with group theory - perhaps Volker Heine's "Group Theory in Q.M." is a good start. But Butler proves Schur's lemmas on page 12, so be prepared!. The Tables have been more than useful as well, they generalize the 3-j, and 6-j symbols (and there are a few 9-j and 12-j's as well) for groups below SO3, which have already been tabulated in the Rotenberg-Bevins-Metropolis...classic. These extra 3-j's become necessary in spectroscopic problems when the actual point group symmetry is invoked. You will require Rotenberg et al., or else use the 3-j/6-j algorithm in Mathematica for the SO3 case, since Butler does not provide them. Butler develops a theorem for the agreement of parity between his 'natural labels' of irreducible representations and that of the underlying interaction which I have employed in considering the selection rules on superexchange matrix elements, but it is in fact a very general theorem. I have heard it said from recent physics graduates that they no longer learn group theory. That is a shame, and may very well change in the future, as these methods are quite powerful and can be enlarged to investigate the dynamics of statistical systems, not just simple, spherical ('atomic') quantum systems. So, if you're one of these deprived physics graduates, this volume is a real eye-opener, as it will introduce another way of thinking about physical problems to you, and that boon is sometimes worth it in itself, just as learning path integral techniques often is, even when they don't help you solve any particular problem, they nonetheless help you gain a fresh perspective on any particular problem you might be confronted with.
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