Excellent Text | Principles of Quantum Mechanics

Perfect on its aim | Principles of Quantum Mechanics | R. Shankar

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	• Principles of Quantum Mechanics R. Shankar Springer, 1994 - 694 pages average customer review:based on 59 reviews view larger image
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highly recommended

A Well-Written Introduction

This is probably the best book to learn the subject at an advanced undergraduate or a first-year graduate level. It is clearly written, doesn't skip steps in derivations, doesn't assume any prior knowledge of quantum mechanics (unlike Sakurai), and is reasonably complete. The last chapter on path integrals and applications, in particular, is outstanding.

Answers to end-of-chapter problems are provided, making this book a good choice for self-study.

There are, unfortunately, two drawbacks. The first and by far the more significant one is that the problems are, generally, too easy. While simple confidence-building exercises are important and their presence is never unwelcome, virtually every problem here is of this type. Thus, an inexperienced student going through the book on his own might fall victim to a false sense of mastery. This is indeed the one area where a supplement is particularly helpful. The second and relatively minor drawback is that some topics aren't developed in as much depth as they are in similar books. Compare, for example, Sakurai's exemplary chapter on angular momentum to Shankar's merely adequate treatment.

In all, a fine book to learn from and a useful book to have.

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Excellent Text

Having been scouring my old college text and many other books on Quantum Mechanics I found them lacking in their ability to explain the mathematics behind the theory. This text approaches the subject by way of Linear Algebra and Vector Spaces.
Shankar's Text lays everything out brilliantly buy hitting the mathmatics FIRST then going into the theory. I am working my way through the first chapter on the mathematics which is very clear so I have no doubts that the text on the theory will be just as lucid.
Once you can turn the crank of the mathematics then the theory will be open to study for you. That's the trick.
Excellent text for someone who has had either a good grounding in linear algebra or undergraduate QM.

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Perfect on its aim

Quatum Mechanics is conceptually hard enough itself to get more trouble than necessary trying to assimilate the language it's written in - maths. For someone who has struggled with Cohen-Tanoudji to understand all the mathematical apparatus concerning the description of quantum mechanical phenomena, it felt quite comforting to end up with this book.

Of course this is not Cohen-Tanoudji, and you cannot find in it everything you would look for, but it doesn't pretend to neither. This is, more than a pure physics text, a progressive approach to Dirac notation, Hilbert spaces and not-easy-to-go-with concepts whose understanding is vital to get along with everything that comes later.

In my opinion, this is a beginning, and a rather good one. But that's it. Do not expect for more. You'll have the fundamentals of Hydrogen atom, momentum coupling, spin, perturbation theory, etc. and the maths underneath them.

For that reason, I find the price a bit high, and would not recommend it for a graduate level, maybe just in case quantum is not your primary field of work.

A "but": despite it's supposedly simple and self-contained, it sometimes lacks deeper explanations of results the author gets to by apparently 'divine intervention'.

For learning purposes, starting students will find a useful tool to deal with Quantum Mechanics and its complexity.

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An impressive QM book.

I am a lecturer who teach QM mostly. I've read various QM books so far. Apart from being reader-friendly, Shankar's book touches my mind in several points. Dirac equation (chapter20) is superbly written. The book explains very well how the matrices Alpha's and Beta are chosen to form the Dirac Hamiltonian. The fact that they are traceless and they have eigenvalues +1 or -1 is awesome. Furthermore, it gives a clear and beautiful picture that Dirac equation can reduce to Schroedinger one with E&M interaction plus H-fine structure whereas most other QM books treat this in more-unfriendly ways. The first 7 chapters may be read by advanced undergrad students. Stern-Gerlach experiment is well explained compared with averaged QM book. Another touching point is the Chapter of spin. Most QM books seem not to mention the linear independence of 4 Pauli matrices clearly whereas it is nicely proved in Shankar's book. The seeming drawback in my viewpoint is that path integrals should not be treated too much in a QM book(2 Chapters). It should be contained in the books of special fields. Something like 2nd quantization or field operator should be instead. However, in overall, this QM book is quite valuable to our academic world, and deserves 5 stars.

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Reviews from the First Edition:

"An excellent text ? The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)

"No matter how gently one introduces students to the concept of Dirac?s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)

Reviews of the Second Edition:

"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. ? It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)

R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:

- Clear, accessible treatment of underlying mathematics

- A review of Newtonian, Lagrangian, and Hamiltonian mechanics

- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates

- Unsurpassed coverage of path integrals and their relevance in contemporary physics

The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book?s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

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