Customer Reviews

Angular Momentum in Quantum Mechanics (Investigations in Physics, No 4)

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Since its publication in 1957, Edmonds has been the reference for physicists and chemists interested in angular momentum calculations in molecular, atomic, nuclear and sub-atomic physics. Though it contains some typos in various editions, one famous instance being the reversal of conventions in a couple of key definitions between the 2nd revised printing in 1968 and 3rd printing in 1974, it remains a standard for a two generations of scientists.

One of the most impressive things about this book is that it contains no known errors. That's pretty good for a subject which is highly mathematical, and riddled with superscripts, subscripts, primes and double primes.

This is not the most readable introduction to the quantum theory of angular momentum (for that I would have to suggest Richard Zare's book), but it provides a compact and useful introduction covering most of the usual material such as phase relationships, coupling and recoupling relationships (by means of clebsch-gordan coefficients, properties of three-, six- and nine-J symbols). The book is extremely theoretical (not suprisingly) in approach, not actually getting to useful examples until the final chapter, when a few examples of the use of the theory for calculating matrix elements of particular operators are given.

One of the most useful features of the book is the appendices, which give rather detailed summaries of the properties of Clebsch Gordan coefficients, 3-J and 6-J symbols.

This is an extremely useful book. It is a classic in the field. If you have any need for the quantum theory of angular momentum in your research, then this is a must-have volume.

Edmond's book provides a useful, compact, and fairly easy to follow guide to a topic that is all important in quantum mechanics: that of angular momentum. Because particle spin is also angular momentum, an understanding of this topic is extremely important in the proof and application of the Spin Statistics Theorem which allows us to see why spin n+1/2 Fermions differ from integral spin Bosons. Accordingly, this book is listed as a reference in Chapter 5 of Weinberg's venerable The Quantum Theory of Fields (Volume 1), in which the Spin Statistics Theorem receives a very thorough and lucid treatment.

Of particular interest to me is Edmond's treatment of differential operators in spin space on pp.26-27. I have attached the jpeg files for these two pages. If X+ and X- represent the spin eigenvectors u(1/2,1/2) and u(1/2,-1/2) respectively, and d+=d/dX+ and d-=d/X-, the components of spin angular momentum can be expressed as Jx=(h/4pi)(X-d+ + X+d-); Jy=(ih/4pi)(X-d+ - X+d-); Jz=(h/4pi)(X+d+ - X-d-); J+=(h/2pi)X+d-; J-=(h/2pi)X-d+. By manipulating these differential operators, Edmond shows that the basis for the D(j) representation of the angular momentum operator should be proportional to the monomials corresponding to (X+)**(j+m)(X-)**(j-m). Although this sort of argument is put forward by many other books discussing angular momentum, such as Tinkham's Group Theory and Quantum Mechanics, I found the treatment in this book to be somewhat more satisfying.

I need it for the 3nj symbols formula, for those who actually care....:). It is a very well written book. Almost all the formula you need for CG coefficients are available. Unfortunately nowadays you can also find all of them on mathematica-wolfram website.