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5.0 out of 5 stars
A no-nonsense book with a little mathematics., January 30, 2000
In the opening introduction, Dr. Treiman explains that he wanted to write a book on quantum physics that was somewhere between the mathematical treatments one typically finds in graduate and advanced undergraduate texts, and the almost purely philosophical, "no equations allowed" armchair reading so common in the popular press. I believe that Dr. Treiman has been largely successful in achieving this goal, and I found "The Odd Quantum" to be one of the most enjoyable books I've read in a long while.
It's not hard to find books in the popular press such as "Schrodinger's Kittens and the search for reality" that deal with the subject of quantum physics. There are other examples, but all of them share one thing in common -- an almost complete lack of any real quantitative analysis or any equations. Some authors complain that a book's popularity has a kind of mathematical inverse relationship between the number of equations in the book and the number of books sold. The result is a plethora of books that deal qualitatively with philosophical issues upon which almost anyone will feel qualified to speculate.
Treiman's book is not of that ilk. True, this is not a mathematically rigorous book, nor does it develop many of the mathematical nuances found in modern quantum theory. But the book is no mathematical slouch, either. Without requiring a tremendous amount of mathematical skill, Trieman manages to bring out many of the most interesting aspects of quantum theory with clearly elucidated equations.
It's a little difficult deciding exactly what level of mathematical expertise Treiman had in mind for his readers. On the one hand, he presents Maxwell's equations with apology for the mathematical form, yet in later parts of the book he includes much of the same mathematical formalism (partial differentials, for example) with apparent expectation on the part of the reader. I suspect that his perception of the reader's grasp of mathematics is someone who has at least completed a first semester of calculus. Mathematical subjects covered in the book include integration, differentiation, partial differentiation, and some common mathematical operators. The author develops the linear non-relativistic Schrodinger equation, and if you can handle that level of mathematics the rest of the text should present no problem.
Another feature of this book is its no-nonsense approach. The author does not delve into issues such as parallel worlds, or even too much of the meaning of reality. These are all common subjects in most armchair texts on quantum theory, but Treiman's book pretty much ignores all that in favor of a basic mathematical description of the core issues in quantum mechanics. This is an ideal text as a companion for an introductory class in quantum mechanics, or as a refresher course for those who have studied the subject, but not been actively involved with it since their formal education. Mathematically inclined individuals who have not yet studied quantum physics, but wish a basic understanding of the subject would also enjoy it.
Treiman follows the traditional historical approach. He begins with a review of classical physics, including Newton's law of gravitation, the theory of relativity, conservation of energy, and classical electromagnetism. He then proceeds to outline the basic principles of the "old" quantum physics, including developments around the problem of black-body radiation, early work in spectroscopy, the Rutherford atom, Bohr's quantum model, and De Broglie's matter waves.
With this introduction properly made, Treiman proceeds to describe the foundation of modern quantum mechanics by laying out the two-slit experiment and Schroedinger's wave equation (linear and non-relativistic). There is a nice discussion of the probabilistic interpretation of the Schroedinger equation, and a quite useful summary of the basic rules that define modern quantum mechanics. Treiman also does a good job of laying the foundation in such important areas as commuting observables and how that ties in with the venerated uncertainty principle. As part of this foundational discussion Treiman describes the concept of an operator, and then proceeds to derive several common operators used in quantum physics, such as the Hamiltonian, momentum, and position operators. [I listed them by hand in the back of the book, but it would have been nice had the author summarized these important equations in the text.] The foundational material finishes with discussions on angular orbital momentum, spin, and tunneling.
With the foundations properly established the author proceeds to solve several classic problems in quantum mechanics, including the free particle, particle in a one-dimensional box, and the harmonic oscillator. There is also a very nice discussion about the fermi gas and some important distinctions between fermions and bosons, along with a good summary section describing the quantum numbers and conventions used when describing the energy levels of various atoms.
The book's last chapters include one titled `What's going on?" which delves more into the philosophical issues associated with quantum physics, and a final chapter that deals with quantum fields.
In summary, this is an excellent companion or refresher text. It's a relatively short book, though, having only about 260 pages. I would have enjoyed having more illustrations, and the index is too short. Overall, however, the book is just what I was looking for - something that's not quite intellectual pabulum, but not so mathematically involved that it cannot be read by a hot fire with a cup of tea the hour before bedtime.
Duwayne Anderson, January 30, 2000
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