When I was an undergraduate student in Physics Department, our quantum mechanics textbook was Gasiorowicz's. It was almost twenty years ago, and I changed my major into mathematics. Several years ago, I have restarted to study physics from scratch, reading freshman physics book, books on classical mechanics, electrodynamics, relativity for undergraduates, as well as books for general audience introducing the newest developments in physics. After studying those, I wanted to study quantum mechanics, and chose Griffiths' book as my self-study textbook. When studying quantum mechanics as an undergraduate student, I remember that I got two A+'s in two semester courses. However, by now, I forgot most (more frankly, all) of the things. Before reading Griffiths, I read Susskind's recent popular book on quantum mechanics, as well as watched online lectures by Shankar. The two were extremely helpful to me in terms of getting a big picture.

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.

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