Van der Waerden B.L. Group Theory and Quantum Mechanics
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Springer-Verlag, 1974. — 211 pages.Van der Waerden wrote this book in 1932, about the same epoch of Hermann Weyl's book on group theory, in German. After a staggering gap of 42 (! ) years, he prepared this second edition, this time in English. It's probably the cleanest and most rigorous exposition of group theory ever made "for physicists". The quotes were needed because van der Waerden's slant is mainly towards math, as far as mathematical rigour is concerned. But what a clarity! And what a great choice of topics! After a review of basic quantum mechanics in a rather mathematically rigorous and clean style, it starts with group theory itself. It manages to proof the basic theorems about groups with or without operators, discuss representation theory in the context of observables and symmetries, expose thoroughly Lie groups (translations, rotations and the Lorentz group), spinors and the Dirac equation, and permutations, and introduce briefly molecule spectra, all that in about 200 pages! No time-wasting like most other books, which seem to "over-wrap" the main core of the subject, making it hard to peel. There is a rather large amount of references to heavy Lie group theory and functional analysis' theorems, but here I have to agree with the author that inserting also their proofs wouldn't add anything profitable, because they would be beyond the book's scope and totally out of context. Even in these exclusions we notice the author's wisdom.
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