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# Introduction to Quantum Mechanics

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Review: Griffiths a walking contradiction - Griffiths was my first introduction to quantum mechanics ever. Now that I’ve seen a lot of quantum mechanics, I have to say my opinion of Griffiths as a text to learn from has gone down significantly. I will explain more. The good: Griffiths is really special in my opinion. I really like how accessible this book is. With only knowledge of basic calculus and linear algebra, you can basically get a good understanding of all the closed-form methods in quantum mechanics. When I first self-studied this before taking quantum mechanics, I was surprised at how accessible quantum mechanics was. I’ve always heard it as a very polarizing and strange and esoteric topic but Griffiths kills that notion pretty quickly. And in some ways, he convinces you that quantum mechanics is more natural than classical mechanics. He starts with wave mechanics and chapter 2 starts with particle in a box, simple harmonic oscillator, finite square well, Dirac delta function well and explanations of bound and scattering states. These are basically the only potentials you will ever be able to solve analytically in quantum mechanics. Everything is a variation of these problems or can be approximated by these. Griffiths hands you the keys right away and I appreciate him for making his readership feel empowered and trusting them with heavy machinery right away. And most surprisingly, Griffiths is an extremely good reference text for quantum mechanics. Like it is uncharacteristic for an undgergraduate intro book to be this good as a reference text. He solves out all bound and scattering states and highlights results for quick access. He lays it all out so well that if I’m running simulations or putting something into mathematica and I need to reiterate what previous results were, I look at Griffiths first. And he also does the little things well. His appendix is full of math review (I didn’t need it but it would certainly help for someone who does) and his back cover has integral tables for gaussians over all space (I prefer this to mathematica actually!). Furthermore, Griffiths is extremely self-contained. He basically covers every undergraduate topic in quantum mechanics. All the way from stern-gerlach to time-dependent perturbation theories. That is a huge scope for a self-proclaimed introductory book. I applaud him for being ambitious and trusting the reader. I always look back into Griffiths as a reference because it’s so easy to keep around and to look for quick results stated. The bad: My only issue with this book, but a huge one, is the lack of Dirac notation. He introduces it briefly in chapter 3 but NEVER uses it practically. Dirac notation is slightly harder to learn at first because it requires that one understands a full undergraduate sequence of linear algebra, but it cannot be understated how much easier and less convoluted calculations and proofs get with Dirac notation. I almost find it necessary for a book to use Dirac notation if dealing with anything resembling a state. Griffiths also favors using matrices instead of operators in the abstract and he hands you the machinery without proof. “If it works, use it” is what Griffiths seems to go for, which I admire because it makes quantum mechanics a lot more accessible, but it’s also not as great for someone who seeks a more rigorous foundation than just being able to calculate things. Griffiths foregoes Dirac notation for an ugly spinor/arrow vector notation which I don’t understand at all. No professors nowadays teaches quantum without Dirac notation, nor should they. This makes a lot of the more complicated proofs and derivations more ugly and convoluted. Imagine trying to develop the simple harmonic oscillator’s eigenstates and eigenvalues by plugging in an integral everytime you take an expectation value? That’s a horrible mess. Griffiths also does not talk about the more algebraic and group-theoretic aspects of quantum mechanics like Noether’s theorem and generators and unitary operators. Although this is understandable for an intro book. Overall, great book. Would be perfect with slightly more rigor and Dirac notation but we can’t have everything I guess.
Review: Learning Quantum Mechanics is Difficult - 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.

## Technical Specifications

| Specification | Value |
|---------------|-------|
| ASIN  | 1107179866 |
| Best Sellers Rank | #1,460,949 in Books ( See Top 100 in Books ) #1,128 in Quantum Theory (Books) #12,112 in Science & Mathematics |
| Customer Reviews | 4.6 4.6 out of 5 stars (139) |
| Dimensions  | 7.25 x 1.25 x 10.25 inches |
| Edition  | 2nd |
| ISBN-10  | 9781107179868 |
| ISBN-13  | 978-1107179868 |
| Item Weight  | 2.5 pounds |
| Language  | English |
| Print length  | 465 pages |
| Publication date  | August 16, 2016 |
| Publisher  | Cambridge University Press |

## Images

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## Customer Reviews

### ⭐⭐⭐⭐⭐ Griffiths a walking contradiction
*by A***G on May 3, 2018*

Griffiths was my first introduction to quantum mechanics ever. Now that I’ve seen a lot of quantum mechanics, I have to say my opinion of Griffiths as a text to learn from has gone down significantly. I will explain more. The good: Griffiths is really special in my opinion. I really like how accessible this book is. With only knowledge of basic calculus and linear algebra, you can basically get a good understanding of all the closed-form methods in quantum mechanics. When I first self-studied this before taking quantum mechanics, I was surprised at how accessible quantum mechanics was. I’ve always heard it as a very polarizing and strange and esoteric topic but Griffiths kills that notion pretty quickly. And in some ways, he convinces you that quantum mechanics is more natural than classical mechanics. He starts with wave mechanics and chapter 2 starts with particle in a box, simple harmonic oscillator, finite square well, Dirac delta function well and explanations of bound and scattering states. These are basically the only potentials you will ever be able to solve analytically in quantum mechanics. Everything is a variation of these problems or can be approximated by these. Griffiths hands you the keys right away and I appreciate him for making his readership feel empowered and trusting them with heavy machinery right away. And most surprisingly, Griffiths is an extremely good reference text for quantum mechanics. Like it is uncharacteristic for an undgergraduate intro book to be this good as a reference text. He solves out all bound and scattering states and highlights results for quick access. He lays it all out so well that if I’m running simulations or putting something into mathematica and I need to reiterate what previous results were, I look at Griffiths first. And he also does the little things well. His appendix is full of math review (I didn’t need it but it would certainly help for someone who does) and his back cover has integral tables for gaussians over all space (I prefer this to mathematica actually!). Furthermore, Griffiths is extremely self-contained. He basically covers every undergraduate topic in quantum mechanics. All the way from stern-gerlach to time-dependent perturbation theories. That is a huge scope for a self-proclaimed introductory book. I applaud him for being ambitious and trusting the reader. I always look back into Griffiths as a reference because it’s so easy to keep around and to look for quick results stated. The bad: My only issue with this book, but a huge one, is the lack of Dirac notation. He introduces it briefly in chapter 3 but NEVER uses it practically. Dirac notation is slightly harder to learn at first because it requires that one understands a full undergraduate sequence of linear algebra, but it cannot be understated how much easier and less convoluted calculations and proofs get with Dirac notation. I almost find it necessary for a book to use Dirac notation if dealing with anything resembling a state. Griffiths also favors using matrices instead of operators in the abstract and he hands you the machinery without proof. “If it works, use it” is what Griffiths seems to go for, which I admire because it makes quantum mechanics a lot more accessible, but it’s also not as great for someone who seeks a more rigorous foundation than just being able to calculate things. Griffiths foregoes Dirac notation for an ugly spinor/arrow vector notation which I don’t understand at all. No professors nowadays teaches quantum without Dirac notation, nor should they. This makes a lot of the more complicated proofs and derivations more ugly and convoluted. Imagine trying to develop the simple harmonic oscillator’s eigenstates and eigenvalues by plugging in an integral everytime you take an expectation value? That’s a horrible mess. Griffiths also does not talk about the more algebraic and group-theoretic aspects of quantum mechanics like Noether’s theorem and generators and unitary operators. Although this is understandable for an intro book. Overall, great book. Would be perfect with slightly more rigor and Dirac notation but we can’t have everything I guess.

### ⭐⭐⭐⭐⭐ Learning Quantum Mechanics is Difficult
*by I***E on March 27, 2018*

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.

### ⭐⭐⭐⭐⭐ Griffiths explains the math pretty thoroughly as well
*by D***N on March 30, 2018*

I wouldn't ask for any other book on quantum for undergraduate students. It can be an uphill battle if your math methods skills are not up to snuff, however. Griffiths explains the math pretty thoroughly as well, and he has very succinct, clear ways of teaching that other authors don't have. For example, in learning about the Schrodinger Equation in spherical coordinates, he really lays out the derivations adroitly, always with an adequate explanation. This is an almost purely mathematical book with a limited number of physical and real world examples, however, and that's what you'll be mastering with this text, the mathematics of quantum mechanics. Sometimes he does gloss over concepts you need to know in your classes, but he usually does a great job at filling the gap.

## Frequently Bought Together

- Introduction to Quantum Mechanics
- Quantum Mechanics: Concepts And Applications
- INTRODUCTION TO ELECTRODYNAMICS, 4TH EDITION

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