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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra, by Eugene P. Wigner
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Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Pure and Applied Physics, No. 5) by Eugene P. Wigner. Translated by J. J. Griffin. Series edited by H. S. W. Massey and Keith A. Brueckner. Hardcover published by Academic Press.
- Sales Rank: #907611 in Books
- Published on: 1959-01-01
- Original language: English
- Number of items: 4
- Binding: Hardcover
- 372 pages
Most helpful customer reviews
8 of 8 people found the following review helpful.
The ultimate resource for the fundamentals of group theory as applied to quantum mechanics
By Ulfilas
Eugene Wigner won the 1963 Nobel Prize in Physics, in part due to his contributions to symmetry principles in physics. In reading other books on group theory and quantum physics, you usually find a large number of references to Wigner's book. In fact, other books often state a theorem and then refer to Wigner's book for the proof. For me, I was trying to find a proof that I could understand for the Vector Addition Theorem for angular momentum. The proof involves breaking down the direct product of two angular momentum representations into a sum of irreducible representations--that is, D(i) x D(j) = D(i+j) + ... + D(i-j). For example D(1) x D(1) = D(2) + D(1) + D(0). Wigner gives a simple proof for this theorem on pp.186-187 in which he just rearranges the components of the characters of the representations. I had already read the proofs for this theorem in Tinkham Group Theory and Quantum Mechanics and Heine Group Theory in Quantum Mechanics: An Introduction to Its Present Usage (Dover Books on Physics), but either I could not understand their proofs or I just could not find them convincing. Wigner's proof, however, was clear and understandable. Please note that I have scanned pp.184-189 so that the reader can get a look at Wigner's proof.
0 of 0 people found the following review helpful.
A classical reference in quantum and atomic physics
By Pichierri Fabio
Wigner's book (published in 1959) is an expanded and revised English translation of the book originally published in German in 1931. Starting from vectors and matrices the author moves on to the description of abstract group theory and its application to atomic spectra. This is a classical reference in the field of quantum mechanics and atomic physics which should be consulted by most physicists and chemists although the style is rather concise and the expected reader is someone that has already been exposed to the basic concepts of group theory and quantum mechanics. A nice and more pedagogical book on group theory is McWeeny's "Symmetry: An Introduction to Group Theory and Its Applications" while for those interested in the application of group theory to molecules the book "Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra" by Wilson, Decius, and Cross is highly recommended (both books are published by Dover).
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