Principles of Quantum Mechanics 2nd Edition by R. Shankar (PDF)

Description

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 physicsThe 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Principles of Quantum Mechanics by Shankar is one of the more broadly used texts for introductory quantum mechanics. The level is more mathematical and tackles more deeply most subjects than Griffiths and has chapters on the path integral formulation as well. If one is trying to learn the subject on one’s own this is a solid text. The book is self contained, it has many exercises with solutions for some and as the book is so abundantly used, there are numerous online further discussions of the chapters in the book and solutions to exercise that can be referenced if needed. The intended audience is really upper level undergraduate rather than first year graduate though the material overlaps with first year graduate quantum mechanics but at a slower pace.The author provides a strong mathematical foundation as well as a review of the intermediate classical mechanics including Lagrangian and Hamiltonian formulations that provide the foundation of comparison for classical vs quantum mechanics. The author starts the discussion of quantum mechanics by discussing the failure of classical mechanics and the wave nature of particles and quickly moves on to motivating the postulates of quantum mechanics and the differences between classical and quantum mechanics. As is then typical one dimensional problems are discussed and key concepts like probability current and scattering are introduced early. The author does not solve too many simple potential problems and leaves things like the finite square well as an exercise for the reader. The author then moves on to the harmonic oscillator which is an essential potential to get used to and uses both series and operator methods to show how it can be solved. The author also introduces the path integral formulation in two stages but I don’t believe these are easy on a first reading nor are they as dependable as Sakurai. The author then covers several core topics including the uncertainty principle from a matrix standpoint rather than Fourier analysis. The author introduces tensor product spaces quite early and brings up the features of identical particles. The strongest parts of the book to me were angular momentum and spin. The author starts out by discussing the generators of angular momentum and symmetries of rotation, the approach leads to a natural translation to considering spin later. The coverage of the hydrogen atom is standard and clear. Addition of angular momentum to me was where I got more out of the book relative to other textbooks, the author introduces C-G coefficients clearly and discusses the Wigner-Eckhardt theorem which is a difficult topic to discuss at the level of this book. The author also does a good job introducing the reader to concepts like irreducible representations for angular momentum; thus gently introducing Lie theory without focusing on the math. The chapters on perturbation theory i found on the relative weaker side vs other texts without the best exercises nor as comprehensive as it could have been for a first reading on the subject. Time dependent Perturbation theory I found more clearly covered in Townsend. The chapter on scattering theory is pretty good and follows from a more indepth passing of 1-d scattering contained in the beginning, but certain concepts are not developed as deeply as they could leaving the reader potentially out of their depth in things like Greens functions.Overall this is a good self contained quantum mechanics text. The way the author sets the stage by working through the mathematics that quantum mechanics is formulated with provides a solid foundation that prepares the reader for the subject. The text is readable and referenceable and has the content for a solid 1 year course. As an undergraduate text I have a preference for Townsend over Shankar and as a graduate text I think Sakurai is better (though i have yet to go through most of it). But this is a good textbook that serves a student well.

⭐I was impressed from how clear and well-motivated everything is in this textbook.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 physicsThe 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.

⭐Extremely well written. You will need to be grounded in classical mechanics and have a reasonable grounding in undergrad mathematics to benefit from the book, it is aimed at “all” levels but clearly requires you to come prepared. All the necessary mathematics is covered in this book, as well as revision of key concepts from classical mechanics (Hamiltonian etc.).

⭐The book itself is very good, first chapter builds the mathematical preliminaries, the next two chapters motivated quantum mechanics (from a historical context), this is where I am at. As for the book itself it arrived within a week of ordering in VERY good condition, like new really. I am very happy with this purchase.

⭐As someone with a post graduate in Mathematics I wanted a technical book to teach the basics of QM. This book is just that; an excellent introduction to a fascinating subject.

⭐One of the best textbooks I have ever read. While I have yet to complete the book, the explanations are very detailed and the contents go way beyond what my uni teaches (at least for a 3rd year physics undergrad).The mathematics is rather rigorous and the author’s writing style is easy to understand. Love it.

⭐A beautifully written book. The only text I have seen which introduces the reader to the postulates of quantum mechanics properly and rigorously, the exercises aren’t bad either.

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