book review

Quantum Mechanics textbooks
Reviewed by: T.J. Nelson

O kay. You haven't renormalized a Schrödinger equation since 1976. The last time you ever did an integration by parts, people were driving around in Ford Pintos and Jimmy Carter was being held hostage in the White House by Iranians. Suddenly your quantum breaks down and you need to have it repaired. Your local quantum mechanic professes ignorance about such things, and, never having seen it, is skeptical that your quantum even exists, let alone whether it can be repaired. So you have to read a book. But which one?

Introduction to Quantum Mechanics
by David J. Griffiths

G riffiths is an introductory textbook on quantum mechanics that is written with good clarity and simplicity. The author provides anecdotal details that enhance the reader's intuitive understanding of the subject. However, there are no worked examples in the book, and the answers to the problems are available only to instructors. For most subjects this would not be a serious drawback, but physics is not one of those subjects. Physics is the study of phenomena that can be studied mathematically. The concepts in physics are relatively few in number and relatively simple, but the student must learn how to manipulate the equations to solve problems. This can only be learned by working through the exercises. Unfortunately, the absence of worked examples in Griffiths' book makes it impossible for readers to check their answers, making the book useless outside of a classroom setting. The book also is not particularly rigorous. However, in practice this should not pose too much of a problem since a qualified instructor would be essential for this 394-page book to be useful as anything more than a doorstop. (Indeed, I have found that this book is the perfect size for keeping my door open.)

Principles of Quantum Mechanics, 2nd ed.
by R. Shankar

S hankar starts out with the basic mathematical tools needed to understand quantum mechanics. Shankar's book is well written, and is far friendlier than Griffiths for students who are learning the subject on their own, or who are returning to it later after moving on to some other field. Many elementary aspects of QM, such as Dirac's ugly 'ket' notation, create endless problems for students schooled in statistics or information theory, where the same notation is employed with quite different meanings. This 676-page book introduces ket notation from the very beginning. Bigger is not necessarily better, however, and this book starts at a lower level than the other books, making the pace slow. QM is not introduced until page 115. However, this book does contain solved problems, and covers Feynman path integrals more thoroughly than the other books.

Quantum Theory: Concepts and Methods
by A. Peres

N either the writing style nor the print quality of this book is in the same class as the previous books. Peres has an idiosyncratic approach to physics that is reflected in a more haphazard coverage of the field. The author expresses negative opinions about the more exotic aspects of QM (such as the many-worlds theory) throughout the book. This may tend to demoralize some readers. However, the book does cover topics like Bell's Inequality, information theory, and the Kochen-Specker theorem.

Problems in Quantum Mechanics
by I.I. Gol'dman and V.D. Krivchenkov

S peaking of old-fashioned, this one is a reprint of an old 1963 book that focuses on perturbation matrices. The print quality is significantly poorer than the other books, but if you're stuck on this problem (which is an important and difficult one), it's very cheap.

Quantum Mechanics: Concepts and Applications
by Nouredine Zettili

T his book is almost as big as Shankar (648 vs 676 pages), but is crammed full of solved problems. Most of the problems are more than just of the "Prove this equation" type, and like Sakurai, relate to its experimental basis, and do so without sacrificing rigor. The only drawback to this book, aside from being a paperback, is that, like the other books reviewed here, it doesn't cover more exotic topics like hidden variables or the role of the observer. However, this book covers both the theory and problem solving in an integrated way. The solutions to the problems are mostly easy to follow, even if your math is rusty. However, the author sometimes gives the wrong starting point for solving the problems; a book like Handbook of Mathematics by Bronshtein and Semendyayav is highly recommended to avoid hours of head-scratching. Because familiarity with basic formulas from physics is also assumed, it also helps to have a copy of Handbook of Physics or a regular physics textbook like Fundamentals of Physics by Halliday, Resnick, and Walker on hand. Because the examples tend to break up the text, the writing style is less engaging than that in Shankar or Griffiths. But, of course, none of these books is intended to be Shakespeare; and to be fair, Shakespeare never gave any worked examples for calculating eigenfunctions of orbital angular momentum, and most of his plays barely even mention the Wentzel-Kramers-Brillouin method for calculating wave functions of a particle.

Modern Quantum Mechanics
by J.J. Sakurai

T his nicely-printed and well-written book is distinguished by a greater emphasis on actual experimental phenomena than most other books. Unlike the other books described here, Sakurai's book touches on important questions like Bell's Inequality. The material is also introduced at a higher level than Griffiths and Shankar, with lots of mathematics, but suffers from the same problem: lots of problems, precious few answers. Sakurai often gives concise verbal explanations of what each thing actually means. This is counterbalanced by an annoying tendency to pull equations out of a hat and skip steps in his derivations. This book, while much better than Griffiths, would still be useful only in a classroom setting or in conjunction with some other book that contains worked examples and derivations whose steps are explained better.

Schaum's Outlines of Theory and Problems in Quantum Mechanics

T his is an ugly book printed on cheap newsprint-like paper, like that found in SAT booklets, and is aimed at struggling undergraduate students practicing for exams. Very little theory; mostly solved problems with a few badly-drawn diagrams. Also has a short chapter in numerical methods that includes snippets of Fortran code.

Anoher textbook is the two-volume work by Cohen-Tannoudji et al.. Whichever QM textbook you use, you will probably need to bounce from one to the other many times before finding one that describes any given topic with any degree of clarity. It is obvious that each of these books sucks in its own unique and wonderful way. Proof of this is left as an exercise for the reader.