Customer Reviews

The Odd Quantum

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4 star:		(2)
3 star:		(3)
2 star:		(0)
1 star:		(0)

 

 

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

I'll just add that there's definitely a problem with an inconsistent level of sophistication in the mathematics. I remember freshman calculus pretty well but am hazy on differential equations, and *The Odd Quantum* lost me starting with Schroedinger's equation - just when it's getting to the good stuff! (By contrast there isn't any calculus in the first three chapters.) I'm still looking for something beyond popular science books that's not too technical.

Physics is beautiful. To understand beauty is rewarding. But beauty has its language. Mathematics is the language of physics. Most popular science books avoid mathematics. They focus on long and boring prose that never seem to get to the point. This book is crystal clear, filled with insights and brilliant explanations. The mathematics is here to help. Fear not. This book will surprise you greatly.

It starts easy, you feel good until you hit the foundations. Author dives into Schroedinger's equation and even worse he starts to use a lot "Eigen.****" in the form of value, function, state etc so that you really have to slow down to comprehend clearly. Subject gets deeper and deeper and he himself says similaer to saying "just take it from me as it is correct". Than provides simple problems and solutions. Although the examples are standard that you find in any introductory course textbooks, the thechincal language he uses makes them difficult to follow. I think this book is not as easy as advertised to be. I do not blame anybody remember after all there is phrase that only few people knows what Quantum Mechanics is. You may want to read this book after reading few more introductory books especially with some formulas and calculations. If you do not know what Eigenvalue is,which author does not even define it, than you better read some calculus before you read this book.

I have read many quantum mechanics (QM) books for "popular science readers" that explain QM in very general terms, with little or no mathematics. The "Odd Quantum" promised a bit more, science for the "popular science reader", but with some of the mathematical underpinnings (although not anywhere to the level in even an elementary quantum mechanics text), which was something that I was looking for. This review tries to answer the question of how well did the book achieve this goal. As a point of reference, I did take elementary quantum mechanics about 45 years ago and have some general familiarity with the mathematics used in the book, so I do not consider myself a popular science reader with little or no technical background.

In my opinion half of the book definitely meets the criteria of suitability for someone without a technical background, but the other half does not. The book begins with a review of classical physics and the earliest version of QM. I found this part of the book to be well written, informative and should be appreciated by someone interested in general popular science. Some of the latter part of the book, which deals with particle physics, also fits into this category. Unfortunately, from my perspective at least, a general reader will find the rest of the book well beyond their comfort zone. This "difficult" part of the book begins with the foundations of the "new" QM, the solution to some elementary problems, such as an electron in a box, and finally a discussion of quantum field theories, how they introduce the idea of particles, and the interaction between fields/particles. These discussions use second order differential equations, eigenfunctions/eigenstates/eigenvectors and Hamiltonian energy expressions and operators. If the previous sentence makes no sense to you, then it is my opinion that you will find this half of the book rather indecipherable. I feel that the book would have been greatly improved by a 20-page appendix describing the mathematics of eignenfunctions and Hamiltonian operators (I found a nice two page discussion of this on the internet, so it can be done). The book would also have benefited from the addition of about 30 more pages of discussions of the mathematics of QM and the problems being discussed. I found far too many "it can easily be shown that" comments for my taste. This is fine for a textbook where the teacher can easily show the solution, but not for a book to be read without the benefit of a teacher.

In my opinion, Professor Treiman did not succeed in bring clarity to QM by including the outline of the mathematics, but not the meat of it. In much of the book I got the feeling that I was reading a chapter summary, without the benefit of having read the chapter. Such a summary is great for those who are familiar with the subject and want a comprehensive review, written by an expert. For those readers this is a 5-star book. For someone without a sufficient mathematical or physics background the book is a mixture of 5-star and 1-star material, so for them it would be a 3-star book. I put myself somewhere in the middle, so I am giving it 4-stars. I liked the book, but was disappointed because it was not as useful as I had hoped it would be.

After reading about quantum physics in other popular books (How to Teach Physics to your Dog, Deep Down Things), I was looking for a book with a little more math, because a formula says more than a thousand words, right? Well, I have a masters degree in (computer) science, but unfortunately, my math skills are way too feeble to understand this book. Unfortunately, the author often doesn't explain in words what the formulas mean, so if you don't understand them, this book is pretty much pointless (save for the first two chapters). The author lost me even before delving into the quantum chapters!

So avoid this book if you don't have a solid math background, i.e. you don't have an intuitive understanding of calculus, differential equations, complex numbers, etc.

Finally a book for people who want to understand QM, but don't want to go down to full blown QM-math.
Finally a book which does not just skim over the surface, trying to make QM look like a magic that only QM wizards can understand.
I got tired of books and movies that try to make QM look like a animation show which we can't understand.

But also as some other mentioned after the Schrodinger equation is introduced the explanations of the math got a bit "murky", much harder to grasp. The author expect the reader to know much more than he expected him to know in the previous chapters.