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Principles of Quantum Mechanics, 2nd Edition 2nd Edition
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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.
- ISBN-100306447908
- ISBN-13978-0306447907
- Edition2nd
- PublisherPlenum Press
- Publication dateAugust 31, 1994
- LanguageEnglish
- Dimensions7.32 x 1.81 x 10.24 inches
- Print length694 pages
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Editorial Reviews
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From the Back Cover
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)
- 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.
Product details
- Publisher : Plenum Press; 2nd edition (August 31, 1994)
- Language : English
- Hardcover : 694 pages
- ISBN-10 : 0306447908
- ISBN-13 : 978-0306447907
- Item Weight : 7.47 pounds
- Dimensions : 7.32 x 1.81 x 10.24 inches
- Best Sellers Rank: #54,382 in Books (See Top 100 in Books)
- #10 in Physics of Mechanics
- #13 in Mathematical Physics (Books)
- #52 in Quantum Theory (Books)
- Customer Reviews:
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Here are some of the things I particularly liked about this book, and some of the ways I thought it could have been better.
The first chapter provides the necessary mathematical background for quantum mechanics. It is a long chapter, but very well done. Regardless, make no mistake, you should not attempt this book at all without a solid background in differential equations and linear algebra. This chapter is very helpful though as a review and for fixing notation. I also approved of its stated goal: to put the math first rather than trying to interleave it with the physics. Physics is hard enough without trying to tackle the math and the physics at the same time.
Chapter two is a quick review of classical mechanics. Advanced classical mechanics. If you are not already comfortable with the Lagrangian and Hamiltonian formulations of classical mechanics before you attempt this book, well you probably shouldn't attempt this book. But if you are, this chapter is an excellent and concise review done with an eye towards quantum mechanics.
Chapter four presents quantum mehcanics in a postulatory manner, and builds the subject deductively from there. Of the quantum mechanics books I've read, the ones that proceed in this fashion tend to be clearest, and this one is no exception.
Chapter five presents a collection of one dimensional problems. This chapter is one of the few that I felt could have been better. I did not think there was enough discussion of tunneling and scattering, which struck me as odd. Certainly I have seen other introductions to quantum mechanics do a better job with these topics.
Chapter ten is on systems with more degrees of freedom and covers the tricky subject of identical particles in quantum mechanics. It is a very clear treatment.
Chapters twelve and thirteen extend the treatment to three dimensional systems and the Hydrogen atom in particular. While good, I thought the author could have done a better job building intuition for the special functions that appear in this section of the book, like the spherical harmonics. The author even states that many other books provide graphs and additional information for these very important functions. Ok, so why not this one as well? For a book that is so complete in so many other ways, this omission seemed odd.
Chapters fourteen and fifteen cover spin and the addition of angular momentum. Challenging topics in quantum mechanics. For the most part the discussion is very lucid, and among the best I've seen.
Chapters sixteen through eigthteen cover approximation methods. They are superb. Chapter eighteen is a particular standout here. The discussion of the quantization of the electromagnetic field is outstanding, and very unusual in an introductory book.
Chapter nineteen is on scattering, and is probably the clearest introduction to this (rather tricky) subject I have seen.
Chapter twenty is on the Dirac equation. Almost never seen in an introductory book, this is again an outstanding feature of this work.
Finally, as other reviewers have mentioned, this book discusses path integrals in two chapters: eight and twenty-one. These discussions are five star worthy. This topic is also highly unusual in an introductory book, but as the author points out it is of central importance in contemporary physics.
The last chapter -- twenty-one -- is definitely the most advanced in the book. It disusses the Quantum Hall Effect, the imaginary time formalism, the connections between quantum mechanics, quantum statistical mechanics, and classical statistical mechanics via path integrals, and ends with discussion of fermionic path integrals which are central to quantum field theory. All of these are advanced topics, and the author does an excellent job preparing the reader to tackle them. Kudos!
There are numerous problems throughout, most of which are rather simple.
This is an excellent book for anyone looking really to sink their teeth into QM.
It contains two big chapters on prerequisites(mathematical methods and classical mechanics) which shows that the author is determined in making you actually understand the subject matter. Next, there is a small chapter to motivate the reader to believe that there's something more than just classical mechanics and effectively builds the way towards Quantum Mechanics. Then, at the start of chapter 4, the author gives the postulates of Quantum Mechanics in the clearest way possible; he gives them in the form of a list and he also compares them with the classical mechanics counterparts. This shows how deeply the author has thought about the presentation of his textbook.
In the next chapters, the author proceeds on with the same spirit and never disappoints. He's done an exquisite work!
What surprised me even more is that the author discusses path integrals and symmetries early one, before even getting to the hydrogen atom and approximation methods. Other textbooks leave path integrals and symmetries until later. This way of introducing path integrals and symmetries is much better. Introducing path integrals early on demystifies them; they are not such foreign concepts as they might seem to be when they are presented near the end of a book and after all the fundamentals of QM have been worked out with the canonical formulation. Introducing Symmetries early on helps with always keeping symmetries at the back of our minds, as we should because symmetries are at the heart of physics
The last point which surprised me was that the author also chooses to present some content that is not presented in typical QM textbooks very often. A brilliant example of this is the inclusion of the Berry phase(at a higher level and more effectively than Griffiths' presentation) which is a beautiful and very modern concept that led to important research(for example the 2016 physics Nobel prize). This also illustrates that the author's background has payed off big time. Shankar's research background is broad: from particle physics to condensed matter physics. And this shows from the choice of the material that's found here.
Now, here is an example that shows how well-motivated is everything:
In the introductory chapter(p.46, example 1.8.6), the author gives an example of how to find the normal modes of two coupled oscillators. He showcases how the change of basis to the eigenbasis is essential for solving the problem and understanding the problem. He uses this example to illustrate how the concepts of linear algebra that he explained a few pages back are used in physics. The whole example is written in the Bra-Ket language of Dirac(which is the language of advanced Quantum Mechanics) and thus serves as a very nice motivation of what's to come regarding Quantum Mechanics.
The textbook is full of such pedagogical examples.
It also reads very smoothly, although anyone that hopes to find a writing style similar to Griffiths' will be disappointed; this author chooses a formal but clear writing style which helps avoid babbling(although I like the writing style of Griffiths). And everything is explained in the intuitive way that you expect from a good author.
Lastly, the exercises in this textbook are very carefully chosen. A great example is exercise 7.4.9 on p.213, where the author shows that the association of the momentum operator is not unique and can be something more rather than just the derivative (-id/dx for 1d); we can also add an arbitrary function f(x) and asks the reader to show that this corresponds to a unitary change of basis.
These kinds of exercises are rarely found in textbooks and are, in my opinion at least, the pinnacle of pedagogy that every textbook must try to achieve.
Top reviews from other countries
My only complaint is the small number of worked out solutions to the problems in the appendix. It is quite an old book, for those to whom such trivialities are deal breakers, but then you don't have to be at the cutting edge to treat the basics, do you?
Highly recommended to anyone who, like me, wants to learn only so much maths as is absolutely necessary, and not one bit more. Life is too short to learn everything, but understanding quantum mechanics, or understanding you don't understand more clearly than a popular science book can communicate, is surely worth the effort.