Quantum Mechanics textbooks
Reviewed by: T.J. Nelson
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
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
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
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
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
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
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
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.
