Principles of Quantum Mechanics

One of my favourite Quantum Mechanics books. Griffith, Greiner, Landau and Shankar are the real deal.

This is a very clear and enjoyable treatment of quantum mechanics. Coming from a math background, I very much appreciate Shankar's development of the subject from the postulates. He doesn't just show you how to work problems, he teaches you how to think physically (logically) about quantum systems. If you really want to understand the subject, this book is for you. A word of warning, though: To get anything out of this treatment, you have to actually read the book. If you want an encyclopedia that you never actually read, just look stuff up in, this book is not for you. Get Cohen-Tannoudji instead. The first two chapters are especially nice, even though they don't deal with any quantum mechanics. Chapter 1 covers all the math you will need for the rest of the book, leaving you free to think about the physics from then on, and it is actually one of the better treatments out there of some important math methods. Similarly, Chapter 2 gives a good, if abbreviated, treatment of classical mechanics, including Hamiltonian dynamics, conservation laws and symmetries, Poisson brackets, etc. The quantum chapters are on a somewhat higher level than most introductory textbooks, but the writing is so clear they are still accessible. He covers the path-integral formulation and the Dirac equation, which a lot of textbooks don't. He has the best treatment of spin and angular momentum I have ever seen, and he includes a chapter called "Symmetries and Their Consequences" where he shows how conservation of angular momentum follows from rotational invariance, conservation of energy follows from time invariance, etc. I have a number of quantum textbooks, and I like this one the best.

One major complaint I have about many textbooks is that they are not particularly self-contained: often times the texts simply don't develop the subjects you need to know to read the book, instead depending on other texts to do so. To some extent I understand this, you can't teach somebody everything they need to know about differential equations in the first chapter of a classical mechanics book and still leave space for classical mechanics.This text addresses that issue perfectly. The introductory section on linear algebra stands by itself very well, and in my opinion is at least as good as the opening sections of Sakurai on linear algebra. It also provides a section on Hamiltonian and Lagrangian mechanics, which the reader can either skip and refer to later or read through, without really disrupting the continuity of the book.All well and good, it sets up the background for quantum mechanics very well, but the key point is how it addresses quantum mechanics itself. And I have to say that it addresses the subject elegantly. It provides well-written sections that are actually entertaining to read, and presents each problem with the brevity it deserves. With the free particle, Shankar simply gives the propagator and procedes to the next section, which is about all that can be done for the free particle, since the energy eigenstates are not normalizeable. The treatment of the quantum harmonic oscillator is among the most complete I've ever seen, approaching it from every possible angle and devoting an entire chapter to the varied solutions.And all this is done with a great deal of clarity. If the text comes across something you might not understand, Shankar stops and discusses it for a page, going into the physical implications of various solutions and theorems, making you feel comfortable that you actually understand the results and are not merely quoting them.In some areas it seems like Shankar holds back on things, and if you want a little group theory in your quantum you'll have to go to another source to supplement, Sakurai comes to mind. But the Shankar can stand alone as the best overall quantum mechanics textbook I have ever read.

Shankar is one of those rare beasts which attain the perfect mixture of physical insight and rigourous mathematics. The way quantum mechanics is being taught these days is slowly evolving to take into account the recent advances in condensed matter physics and quantum information science. Shankar's book has a thoroughly modern feel to it, which I feel is entirely complementary the new understanding of quantum mechanics currently being developed. Shankar presents the axioms of quantum mechanics early, just after going through a self-contained introduction to the mathematics required to understand the content of the book. The only criticism I have of this book is that the motivation for the axioms seems a little weak. He then goes through all the standard subjects, eg., angular momentum, scattering theory etc. One nice feature is a very clear description of Feynman's path integral. Another great feature of this book is the inclusion of a broad selection of exercises, most of which are trivial (and hence confidence-building), but still *interesting*. There are partial solutions as well.One of the most unexpected features of this book is that, unlike most learning books, it does not become useless once you have gone through it. At the end of the book there is a beautiful chapter on advanced topics, including, the quantum Hall effect, the Berry phase, and Feynman's path integral as applied to condensed matter physics. The small section on the integral and fractional quantum Hall effects is surely the quickest way to learn about the basic effect.Shankar will continually reward the reader, from the moment you pick it up to learn quantum mechanics for the first time, to the point where you begin research in condensed matter physics, high energy physics, quantum information or any other branch of physics.

This is THE Quantum Mechanics Text. We used it for the 98-99 graduate course in QM at UC Santa Barbara. I had never really studied QM before, and without Shankar's book guiding me, I don't think I would have made it through the course. QM is not an easy subject, but if you have a genuine desire to learn, Shankar's book will make the experience as painless as possible, not to mention a hell of a lot of fun! A few notable points of the book: A nice physicist's intro to the elements of functional analysis as needed for Dirac's version of QM- which is what most of the book is based on. A good treatment of Lagrangian and Hamiltonian mechanics that allows one to appreciate the transition from classical mechanics to QM. Postulates first, explanations of them, and then applications later. Also a good intro to Path integrals and field quantization for those that plan to take Quantum Field Theory. Hopefully someday Shankar will write a book on Quantum Field Theory!

How many quantum mechanics textbooks can you think of that have funny jokes in them? Shankar's Principles of Quantum Mechanics has everything a student needs to gain a deep understanding of the fundamentals, including an introduction to the math and notation used in upper-level university quantum mechanics courses, treatment of the uncertainty relations and their origins, angular momentum, the hydrogen atom, perturbation theory, scattering, correspondence between classical and quantum mechanics, and humor. Shankar also explains the context in which quantum mechanics was invented. While the writing is concise, it is full of insightful observations, and numerous irresistable, yet deep, questions to ponder. On the other hand, the explanation of the basics is clear enough and unassuming enough that if you had to, you could learn quantum mechanics just from this book, in spite of an incomprehensible professor. As a graduate student, I still refer to this text whenever basic quantum mechanics questions arise. Although I used this book originally as an undergraduate taking quantum mechanics, it has inspired me more than once as I struggled through graduate problem sets and derivations for my research. I enthusiastically recommend Shankar's book to juniors and seniors at the university level, and to others at a higher level seeking a clear explanation of the fundamentals of quantum mechanics.