Quantum Mechanics (2 vol. set)

The first volume covers in detail the mathematical formalism of quantum mechanics along with its physical motivation, the latter given in the first chapter. And, both in this volume and the second, the authors include a large set of "complements" to each chapter. All of them are very well-written and instructors can fine tune the course using them as needed or as time permits. The treatment of the tensor product of state spaces is especially well done, and the authors give a physical example of its use via the two-dimensional infinite well. Chapter 3 is a very long and absorbing overview of the physical foundations of quantum mechanics. The authors introduce the concept of an 'insufficiently selective measurement device', not found in other textbooks on quantum mechanics, and one that can be integrated easily into discussions of the foundations of quantum mechanics. In the complements to this chapter, the reader will find a sound presentation of gauge invariance in quantum mechanics and a brief overview of the path integral approach to quantization. Due to its importance in quantum field theory, the latter could perhaps be expanded into an entire chapter if a future edition of this book is written. The authors also include a discussion of the physics of a particle in a periodic potential, paving the way for a later course in condensed matter physics. A thorough presentation of the harmonic oscillator is included in Chapter 5 of this volume, and the authors include an elementary discussion of the quantization of the electromagnetic field in a complement to this chapter. And, again anticipating a later study of condensed matter physics, the reader is introduced to the physics of an infinite set of coupled harmonic oscillators, i.e. the physics of phonons. Atomic physics of course is not forgotten by the authors, as they spend an entire chapter on the central potential, and include several excellent complements on atomic orbitals and diatomic molecules. The physics and mathematics of angular momenta in quantum physics is discussed in chapter six, as preparation for the more detailed treatment of spin systems in volume 2.

The authors begin volume 2 with a brief treatment of scattering theory, concentrating mostly on the scattering off a central potential. The authors continue the discussion of angular momenta begun in volume 1 and here show the reader how to deal with the addition of angular momenta. Clebsch-Gordon coefficients, spherical harmonics, and the Wigner-Eckhart theorem are treated in detail.

No doubt the most important topic that the authors treat in these two volumes is on perturbation theory, for it is the calculation of cross sections and other physically relevant quantities and their comparison with experiment that give quantum mechanics its ultimate validity as a physical theory. Chapters 11 and 12 on stationary perturbation theory and the fine and hyperfine structure of the hydrogen atom serve as a good introduction to the methods of perturbation theory. The use of numerical methods and the computer is of course the favored method of calculation these days, and will remain throughout the 21st century. As more powerful machines are built and more sophisticated algorithms are developed, more problems in quantum physics of a nonperturbative nature will be tackled, allowing greater insight into and perhaps changes to quantum mechanics.


The authoritative text accesible to beginners and challenging for graduates alike   July 6, 2005
Rehan Dost (Canada)
17 out of 18 found this review helpful

A very easy introduction to quantum mechanics with supplementary topics designed to complement the basic chapters expanding the material to cover advanced topics such as phonons, etc.

Mathematical formulation is gradually brought to light after the basic ideas are explored. The level of mathematical rigour is adequate with appendices as needed. A degree of vector calculus and linear algebra is presumed but more advanced topics in hilbert space, operator theory, dirac notation and tensor products are developed as needed.

However, most importantly the ideas of quantum mechanics and assumptions are explicitly stated, in fact listed which was refreshing. Often introductory texts fail to bring together all the assumptions and then derive the theory leaving one bewildered. This probably has much to do with the history of quantum mechanics rather than poor literary skills. Regardless it was nice to see and much appreciated.

The problems range from very easy to difficult but solvable with some effort and thought. Most importantly the problems highlight important ideas and basic calculations which serve as models to approach more difficult problems.

The books cannot be read as novels and I suggest completing or at least attempting all the problems if you wish to have a solid understanding of nonrelativitic quantum mechanics.

After reading the book and solving the problems you should be able to state the assumptions of quantum mechanics with experimental proof for such and be fluent in it's mathematical foundations. Consequently, you should be able to approach a solution to most problems encountered in introductory quantum mechanics.

For example you should be able to quantize the appropriate classical quantity ( energy for example in the case of the harmonic oscillator ), find it's eigenvalues and eigenstates and corresponding wave equations ( where appropriate ) and then derive the mean values for various quantities and derive their time evolution etc etc.

I found the book indispensable for further personal study in quantum field theory and a very useful reference for refreshing forgotten ideas.

For those of you with no physics background, like myself, I suggest reading Fenymann lectures in physics vol 1-3 for a brief non-technical overview of the IDEAS of physics. I then suggest reading intro to mechanics by kleppner ( do all the problems ) and then electromagnetism by purcell ( do all the problems ). You should then delve into quantum mechanics ( you may wish to brush up on wave mechanics as well ).

For those of you who disdain mathematics there are a number of quantum mechanics books " for the masses" you can read but none will give a grasp of the topic. You must overcome your fear and learn the basic ideas of mathematics.

The difference is between seeing the sunset and having one described to you.


As complete as a book on QM can get   January 24, 2000
Lindelof David (Geneva, Switzerland)
7 out of 7 found this review helpful

This book starts from scratch and works through every aspects of QM someone who studies QM is supposed to know. My advice would be to read every single line of this book, including the small print explanations and the complements. You'll be amazed at what you'll learn.


Comprehensive, and clear   December 6, 2005
drauh (Boston, MA, USA)
6 out of 6 found this review helpful

I do not understand the reviewers who claim this book gives no exercises or good examples. These books are about the only graduate-level QM books which do. Not only that, they explore more interesting/complex material in their "complements" at the end of each chapter. This is far more than can be said of a book like Sakurai's, say, which is also a standard text.

As someone who likes a little bit of rigor, and a lot of explicit explanation of the correspondence between mathematics, this book does wonders. It strongly emphasizes the linear space nature of QM: as an average student, I liked this approach, though I'll wager that faster students and those with less taste for rigor will find this too slow-going. So many things in QM which seem to be mysteries (e.g. sub-diagonalization) when presented by the average terse graduate text become very clear with the presentation in these books. Yes, the authors tend to be more verbose than other authors of graduate texts, but this is not a shortcoming in my view.

I can't recommend this book enough for the beginning student in QM. Even senior-level undergrads would benefit from using, or skimming, this book. These books do require the reader to have had an advanced calculus class where Fourier methods for solving differential equations were studied: one may be able to learn some QM without it, but it would be a hindrance not to have had it.


Simply the BEST (and the most expensive)   December 17, 1999
7 out of 8 found this review helpful

This is, in my opinion, the best introductory book on non-relativistic quantum mechanics. It starts from the very basics, either on physical or mathematical aspects. It has a wonderful collection of worked out problems where one can really understand the lectures. It's also a great reference.

I just can't figure out Why it is so expensive. I believe I bought it 2 years ago by half the price. (First-hand). Anyway, a must have for every Physics student.