I am often asked to recommend textbooks for quantum mechanics (QM). The book adopted most widely is probably Griffiths. Here, instead of recommending or not recommending this book, I’d like to use Griffiths as an example, to share my view on “what we expect to learn” from a good textbook: in which sense Griffiths is such a good textbook, and what are the components that Griffiths lacks.

In short, Griffiths is a manual, or “Cookbook on Quantum Mechanics”. It’s extremely successful in this regard, but is lacking in many other aspects. If you use Griffiths, it’s important to also use other books to complement its shortcomings.

Here are the details:

(I will be brief on the parts where Griffiths is excellent about, since you can easily find them from the book, but it’s much harder to find out what’s missing from the book):

【Lack of】 Historical developments

Historical development doesn’t have to be included in a textbook, since it is modular and can be written into another book focusing on the history of science or biography. It’s thus totally fine that Griffiths lacks a discussion of history.

Nevertheless, as a reminder, here are things one can learn from the history of science:

(1) Credit: When and by whom did discoveries happen.

(2) Scientists as role models.

(3) Learn from history, to train our problem-solving technique, and more importantly, the taste in identifying problems. This is probably the most important, but in fact more difficult for beginners. Because one has to switch between different paradigms and think as “a scientist at that time”, instead of thinking in our modern mindset/paradigm of science and judge how trivial (or nontrivial) their achievements are.

None of the above is necessary for beginners. Griffiths ignores all of these to keep things simple. This is a good choice for a textbook. (But see any textbook from Steven Weinberg for a different approach.)

【Lack of】 Phenomenology and why the framework

Why quantum mechanics (QM)? Around 1900, humans started to explore the subatomic world. There are many experiments that cannot be explained by classical physics. This is why QM is needed. If there were no such experiments, no one would imagine such quantum mechanical rules, nor would they be necessary.

In Griffiths, many of these experiments are ignored, and many others are introduced only as examples to understand the already-given framework of QM. This is an easy way to learn, from a student’s perspective (so students tend to like it). But from this approach, the true value of these experiments is missing: The importance of these experiments is not that they illustrate how the new paradigm (QM) works, but they are the reasons why the old paradigm (classical mechanics) fails, and why one had to invent quantum mechanical rules. These conflicts and struggles are not present in Griffiths.

Some side remarks:

(1) Note that “why the framework is built” is a logical approach, distinct from the “historical development”: (i) The historical way: history is full of attempts and errors, misunderstandings and beliefs without justification. This is not necessary for a textbook, and can often be confusing. (ii) The logical way: clean up all the confusions and tell the learner as succinctly as possible why we need the theory, including the shortcomings of the classical approach and the ultimate resolution. It’s important that a textbook includes this.

(2) The students have learned “general physics”, and may have learned “modern physics” before learning QM. They may have learned “why QM” there already. That’s probably true. But it may be better if a QM textbook does not assume that the students have understood “why QM” extremely well before they take a proper QM course. This is similar to not assuming that the students have learned calculus and linear algebra very well already (Griffiths does a fantastic job in not assuming that the students have perfect math background).

(3) An engineer may have different motivations for learning QM, compared to a physicist. An engineer may learn QM to solve a practical problem, such as how to reduce tunneling effects when chips are made smaller. For these practical needs (again, cookbook), Griffiths is a more efficient approach. But having said that, an engineer may find physics interesting (instead of only useful). And for this reason, “why QM” is still as important as “what is QM”.

【Not great】 The theoretical framework

Griffiths starts from the Schrödinger equation: Providing the equation as the starting point and explain what each term means.

This is an efficient way of learning “QM for the motion of a particle”. However, this mixes up different postulates of QM, and introduces impediments for a deeper understand QM:

(1) Kinematics vs Dynamics: The typical starting point of understanding physics is kinematics – how to identify “what is the system to study”, for example “position and velocity in classical mechanics”. After kinematics is understood, we proceed to dynamics – how the system evolves with time. Griffiths’s approach of starting with dynamics (Schrödinger equation) is unconventional, and in my opinion, not the clearest for understanding.

(2) Many aspects of QM reflect other independent postulates that do not follow from the Schrödinger equation, but just that the Schrödinger equation is consistent with these postulates. In particular: (i) Linearity (superposition) is a different principle. It’s indeed consistent with the fact that the Schrödinger equation is a linear differential equation. But linearity is true starting from the kinematic level, and is so important that it deserves to be understood separately (for example, entanglement). (ii) The momentum operator. Griffiths starts with a Schrödinger equation which already replaced momentum by -iħ∂. Thus, momentum appears as a derived concept instead of fundamental (well, momentum could arise more fundamentally from symmetry, but not from the Schrödinger equation). Again, this obscures facts such that the uncertainty principle holds at the kinematic level.

(3) By hiding the postulates (especially by providing the particular particle motion Hamiltonian as the starting point), it’s more difficult to generalize “Griffiths’s framework QM”, to apply it to more general systems. For example: (i) Spin. Spin is introduced as an “add-on” in Griffiths. But in fact it’s a different system that QM explains – which becomes increasingly important in the era of quantum information and quantum computing. (ii) Quantum field theory (QFT). I used to think QFT is very different from QM (that’s not the fault of Griffiths since I got this misconception elsewhere) until I realized that the Hamiltonian in the Schrödinger equation can take other forms instead of that of the non-relativistic particle. If the postulates of the QM framework are properly imposed, one instead sees that QFT is just applying QM to relativistic fields.

(4) Related to (3), as a by-product of promoting the Schrödinger equation, the “quantum state” is naturally described as a “wave function”. The introduction of the Dirac notation (and associated math of Hilbert space in general, not only for the motion of a particle) is delayed, and its importance is downgraded.

Having that said, the “Griffiths’s framework” is easy to learn, and as a matter of fact, you may have learned that already. I hope that, at least this is not the only framework of QM in your mind, and you can switch to a more solid one once you understand QM more deeply (this is in general very important for learning, not only for QM and not even only for physics).

【Good】 Naming of concepts and mechanisms

Names and conventions are not crucial to the inner logic of the theory. But proper names and conventions are indeed helpful for understanding. Griffiths makes good reference to different concepts (such as “the generalized statistical interpretation”, “the generalized uncertainty principle” to make the boundaries of concepts sharp), which is helpful for beginners.

【Excellent】Solving technical problems

Griffiths is very clear and detailed in solving technical problems. Great for beginners to follow.

【Excellent】Weak assumption on prerequisite math

Griffiths does not assume that you have a strong background in calculus, and does not assume that you know linear algebra at all. This is very helpful since students often forget the content of the prerequisite courses even if they have learned them. This difficulty is very well resolved by Griffiths.

【Not great】Get prepared to subsequent courses

As mentioned above, since the theoretical framework is not put in a modular way, this introduces unnecessary difficulties for students to learn subsequent courses such as quantum information or quantum field theory.

【Not great】Transferable math and physical skills

Physics majors may not have a career in physics in the future. They may succeed in other disciplines using their mathematical and physical skills. For the skills to be transferable, we need not only a cookbook, but more about why the questions are important, and the ideas around solving them before coming to the technical solution. Griffiths does not put enough emphasis on these aspects.

【Excellent】Problem set

Griffiths provides a great set of homework problems for students to work out. And the difficulty levels are marked clearly so that one can arrange their time and efforts to solve these problems.

【Excellent】Prepare for standardized exams

Since Griffiths is great in solving technical problems, and (unfortunately) almost the only thing that standardized exams can test is solving technical problems, Griffiths is great for this purpose.

Unfortunately but true, students were often pushed to learn faster than the pace that they can learn well. For example, they would like to know some quantum mechanics to do well in the middle school physics Olympiads (this is a fault of the problem setters of these competitions). Griffiths is a good book to learn QM fast (but please come back to understand it deeper at a later time).

【Excellent】The feeling of learning

It’s important to give students “the feeling of learning”, to encourage them to learn. The definiteness, clarity and naming scopes that Griffiths offers provides the students the feeling of learning.

However, one should realize that some “feelings of learn” are real, some artificial and some are fake. One should not be satisfied by the fake feeling of learning (though there’s nothing wrong to feel more willing to learn):

(1) Learn only the names. As discussed, Griffiths is good at defining concepts for the purpose of making statements sharp, for the ease of further understanding of physics. But if one stops at learning these names and feels happy that one has learned these names, it’s not helpful.

(2) Oversimplified story for deeper problems. For example, as mentioned, in Griffiths, the key experiments in the history are often introduced as examples of applying the already-developed framework. The students feel that they have understood these experiments clearly, but in fact missed the true value and importance of these experiments. There are different reasons for a concept to be difficult in one textbook but easier in another: (i) the easier textbook introduced it well; and (ii) the easier textbook used an oversimplified introduction. It’s very important to tell the difference.

【Excellent】Online materials and study groups

Since Griffiths is so popular, there are plenty of online materials such as study sharing videos, solutions of problems and discussions with reference to this book. One can also find peers to study with. This is a great advantage for any widely adopted book including Griffiths. So don’t forget to take advantage of this.

Conclusion

As already mentioned (but in case you don’t want to scroll up): in my opinion, Griffiths is a great manual on how to solve problems using quantum mechanics. But it lacks a broader view in the construction of the theory, and depth in understanding QM. Thus, if you’d like to learn QM well (instead of only doing well in exams), it should be complemented by other books.

Which book do you prefer/recommend? Share your opinion with us.