- Paperback: 496 pages
- Publisher: Pearson Education; International Edition edition (2015)
- Language: English
- ISBN-10: 9332542899
- ISBN-13: 978-9332542891
- Package Dimensions: 9.2 x 6.8 x 1.2 inches
- Shipping Weight: 1.3 pounds (View shipping rates and policies)
- Average Customer Review: 297 customer reviews
- Amazon Best Sellers Rank: #98,417 in Books (See Top 100 in Books)
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Introduction to Quantum Mechanics (2nd Edition) Paperback Economy edition by. David J. Griffiths Paperback – 2015
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It was difficult to read Griffiths' book. Among the physics books that I have read, this book took me the longest time. Since I believed that quantum mechanics would be necessary for my future research, I proceeded with a firm perseverance. Whereas I solved few problems when I read other physics books, I solved a lot of them reading Griffiths' book.
In the remainder of this review, I will talk about some bad points, good points, as well as discuss several questions.
1. In the section introducing the expectation value of an operator with respect to a given wave function, the book deals with time derivatives of the expectation values of position and momentum operators. In the calculations, integration by parts is employed. But if we carefully inspect the calculations, we will discover the unspoken assumption that, in the cases of the problems, a wave function and its spatial derivatives very rapidly go to zero near at infinity. However, I don't think that this is a big shortcoming of the book. Reading the book, I agreed with the author saying, in Preface, "But whatever you do, don't let the mathematics -- which, for us, is only a tool -- interfere with the physics."
2. On page 116, there is a problem: how long does it take a free-particle wave packet to pass by a particular point? Really interesting. Still, I think that the book should have referred to momentum like; how long does it take a free-particle wave packet to pass by a particular point? The free particle has momentum p with uncertainty delta p around p.
3. Although I read the parts on spin and fermions several times, I have a difficulty in understanding the parts clearly. I think that, to some extent, this is due to author's writing style. In the relevant section, he starts explaining fermions using position wave function. Almost 10 pages afterwards, he says, "But wait! We have been ignoring spin. The complete state of the electron includes not only its position wave function, but also a spinor, describing the orientation of its spin." And, in a footnote, the author adds, "In the absence of coupling between spin and position, we are free to assume that the state is separable in its spin and spatial coordinates [...] In the presence of coupling, the general state would take the form of a linear combination". Thus, at this point, readers should be able to understand all the presented arguments of previous 10 pages in this new precise point of views.
4. In a section introducing geometric phase, the author says "Now the wave function depends on t because some parameter R(t) in the Hamiltonian that is changing with time." But I couldn't understand why R should depend only on time, but not depend on spatial coordinates. Leaving this question behind, I proceeded to read. After reading some pages, I concluded that it probably be an assumption. This is unclear until now. In the book, there are several places of similar ambiguity.
5. According to the definitions of the uncertainties of energy and time, we can check whether the energy-time uncertainty principle holds. However, the definitions seem to require some messy calculations. I think that, practically, we need an intuitive understanding of the energy-time uncertainty principle. The book focuses on this problem, and provides some examples; yet, the examples were not so helpful to me. In particular, I had a difficulty in understanding why the uncertainty of time as defined can be interpreted as the amount of time it takes the expectation value of an operator (it depends on a given operator) to change by one standard deviation or as amount of time it takes in changing significantly (page 116).
From here are good points.
6. As in his electrodynamics book, Griffiths is very kind in introducing new materials. For example, beginning Section 2.2 The Infinite Square Well, he explains why we should study the case where the potential is infinite square well.
"This potential is artificial, of course, but I urge you to treat it with respect. Despite its simplicity -- or rather, precisely because of its simplicity -- it serves as a wonderfully accessible test case for all the fancy machinery that comes later. We'll refer back to it frequently."
7. The most impressive thing about the book is that it teaches us that there is no free particle with a definite energy. For example, an electron that interacts with nothing is a free particle. In classical mechanics, a free particle can have a definite velocity v, and in that case, it has a definite energy m v^2 /2. As far as I remember, no book pointed out this fact.
8. There is another similar instance. In the section introducing the energy-time uncertainty principle, it says. "The Schrodinger equation is explicitly non-relativistic: It treats t and x on a very unequal footing [...] My purpose now is to derive the energy-time uncertainty principle, and in the course of that derivation to persuade you that it is really an altogether different beast, whose superficial resemblance to the position-momentum uncertainty principle is actually quite misleading [...] Time itself is not a dynamical variable (not, at any rate, in a nonrelativistic theory): You don't go out and measure the "time" of a particle, as you might its position or its energy." I have never seen this wonderful explanation in other sources.
9. If you are interested in quantum mechanics, you probably know the paradox of the Schrodinger's cat. It's a very interesting paradox and, in each book, each author suggests a solution to the paradox. However, I couldn't totally agree with any author except Griffiths'. His solution is concrete, reasonable and clear (at least to me).
Now, two questions. If anyone answers to them, I would really appreciate it.
10. The book uses the fact that the expectation value of the angular momentum L_x (and L_y also) with respect to each eigenstate of L_z is 0 without proving it. For several eigenstates of L_z, this may be confirmed by direct calculations using the fact that an eigenstate of L_z is a spherical harmonic. However, its actual calculations appear to be truly messy. I suspect that there could be a simpler method. In particular, I want to know whether we can obtain the result using only the fundamental relations for angular momentum.
11. In Problem 6.15, we are asked to show that p^2 and p^4 are hermitian. However, we already know that p is hermitian and for two commuting hermitian operators, their product is hermitian. From this, it is obvious that p^2 and p^4 are hermitian. What I don't understand is why we need to prove that they are hermitian.
To me, reading the book was a truly valuable experience. Now, I am reading another quantum mechanics book as well so that to gain a deeper and more comprehensive understanding of quantum mechanics.
First, when is this book useful?
Based on the American educational system: when you're an undergrad student in physics, that is when you've already been exposed to the origins of quantum mechanics through a class often called "modern physics", and have some basics in calculus and linear algebra. But most importantly: if you intend to study physics further, because if you're just in for a tasting go for Susskind's or something similar.
Now if you're a demanding or unusually advanced undergraduate student: relax !!!
You will get to read many other books about QM so don't ask this one to be what it's not claiming to be:
This is not an advanced text and by no means sufficient by itself if you're really committed to studying physics; it is not completely introductory either in the sense that you won't learn about the history of the subject or won't get a purely axiomatic, rigorous approach either. It is designed to make you USE quantum mechanics, sometimes (yes!) even before it tells you what you're doing, so that part of your deeper understanding is built out of your own experience studying examples or working through problems. This said, it also provides good insights and often takes the simplest route to make a point, with a language that i find as entertaining and clear as in his E&M book.
Now studying QM will always be a tricky business because there are so many ways to approach the subject and try to make sense of it, while our brain is truly wired for classical mechanics. You will find the book that does it for you at some point but will have to read several of them no matter what: if you don't get a kick out of this one go somewhere else, but i personally found it extremely helpful and clear. My graduate text was Weinberg, which is fantastic when you're an advanced grad student but almost unreadable when you're not and i heavily relied on Griffiths and some other, popular intermediate books, to help decipher it.
So this is a truly intermediate text and will take you to the meatier treatments of such as Sakurai, Merzbacher, Cohen-Tannoudji and others like a charm; if not, then just go straight to them. And if you're a Vulcan or a mathematician go straight to Weinberg!
I sold off most of my physics text books upon finishing the courses which required them, but I've kept my copy of Griffiths long past graduation, and recommend it to anyone who's interested in an intro to quantum and is willing to do the mathematical legwork to really understand the subject.
This is a huge problem, and these misprints caused me to waste hours of my time solving problems that didn't actually make any sense because some of the symbols were altered.
If you have any commitment to quantum physics beyond a passing interest, you're really gonna want the more expensive hardcover edition of the book, which is what I bought after a month of frustration with this version.