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I took quantum mechanics from our school's electrical engineering department. It was a grad level class designed for students working in device physics, thus it covered a lot of materials: from the basics (Schrodinger's equation, tunneling, the harmonic oscillator), to statistical physics (variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions), as well as some solid state physics basics (simple models for metals, semiconductors).

I then went on to take solid state physics, which used Ashcroft&Mermin, and Lundstrom.

Now I no longer plan to work in device physics for my PhD, but I still want to have a good understanding of QM and Solid state physics.

I was working through the Griffith text, hoping to graduate toward the Shankar text when I came across Dirac's book. It seemed really elegant and focuses on intuition first. I was wondering if anyone would recommend going through Dirac's text before going to Griffith's? It makes more sense to me but most curriculums never even touches Dirac's book.

What are the advantages of studying Dirac's Principles of Quantum Mechanics?

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    $\begingroup$ Griffith is an undergrad physics text, and Dirac is graduate lecture notes -- but nowhere near the depth/seriousness of Sakurai. Dirac is unnecessary if you have the other two... So if Griffith is boring you, go to Sakurai (which, if too hard, go to Shankar). $\endgroup$
    – Chris Gerig
    Commented Jun 15, 2012 at 3:07
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    $\begingroup$ Dirac's classic (on which we get too many confused questions on this site) is subtle and requires a disciplined mind. It is not an introduction. Like Feynman's lectures VIII, it is most useful after you have learned quantum mechanics, forcing you to rearrange your prejudices.... $\endgroup$
    – Cosmas Zachos
    Commented Apr 12 at 14:37

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Read Dirac's book. It is a complete introduction to quantum mechanics, done very elegantly and very physically, with the type of insight that only a founder can give. There is no substitute. Dirac was never used as a textbook, because it is too good, people don't assign good books in elementary classes.

The only things that you need to read in other places are the path integral, which is covered well in Yourgrau and Mandelstam and Polchinsky's string theory books, and ironically the Dirac equation, which you need to work out for yourself, because I don't know a great source.

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  • $\begingroup$ Dirac's book is an introduction to QM for researchers and grad students. It was never used as a text book because he didn't have experience as a teacher of undergraduates and the problems they face; hence there's no exercises in the book. Even Feynman didn't understand Dirac's book when he read it as an undergraduate. The main thing going for it from what I've read is his more abstract view of the subject. Definitely a book only to be read by those with a good understanding of Hamiltonian mechanics and complex vector spaces (which he assumes the reader already knows about) $\endgroup$
    – Physiks lover
    Commented Apr 3, 2015 at 20:27
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    $\begingroup$ @physicslover: Young Feynman had issues due to his philosophy that one must rediscover everything (true, but he overdoes it). He eventually redid QM, via the path integral. Dirac's book is best read in parallel with Feynman and Heisenberg's original papers (Dreimannarbeit too). The physical picture can be lost if you don't know the old quantum theory and the stuff that's now on Wikipedia under "Matrix Mechanics". But given this stuff, Feynman's vol III, Wikipedia, Dirac is a very good intro to canonical QM. The only part that is not so great is the QED, but even that covers Dirac gauge well. $\endgroup$
    – Ron Maimon
    Commented Apr 4, 2015 at 17:05
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    $\begingroup$ @physicslover: Disclaimer: I learned from Dirac. I made up my own exercises by scrounging undergrad books, writing simple programs, and trying to understand chemistry and so on. Dirac was very good for showing how to use formal methods to guide physical intuition, because Dirac's arguments are extremely formal, guided by mathematical identities, e.g. his clever but nearly physically meaningless derivation of the canonical commutation relations in the early intro chapters. The perturbation theory there is excellent, and you can make up your own exercises easily by perturbing the HO. $\endgroup$
    – Ron Maimon
    Commented Apr 4, 2015 at 17:10
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Dirac is definitely worth reading, but you don't necessarily need to read it before you work through either/both of the others. You may even find it useful to read it (again) after working through the others. I would actually say that the three texts are linearly independent; they each have their own strengths and weaknesses. Dirac's explanation of the formalism is fantastic, and his solutions of the simple problems actually makes them comprehensible. The class I used it for stooped using it after the chapter on perturbation theory, so I don't know how good the later chapters are. Griffiths is typically used for physics undergrads who have some physics, but haven't necessarily gotten to all the math that they'll need. It's probably the best of the three for that. As mentioned already, Shankar is typically used for grad classes, but my undergrad class used it. You don't necessarily need to do Griffiths before you do Shankar. Shankar spends a lot of time going through the mathematical formalism, so if you're uncomfortable with any of that, you'll either get comfortable with it or decide to drop back to Griffiths. A really good check is to try to work your way through the problems in Chapter 1.

One big downside to Dirac is that it doesn't contain any problems. So if you want problems to work, you'll have to either pull them out of the other two, or find some on the internet. Dirac's book does discuss the Dirac equation (though see @Ron Maimon's comment below). He does not discuss Feynman path integrals. Griffiths discusses neither of those two. Shankar discusses both. I also just noticed that Griffiths has a section on solids, which includes Bloch's theorem and band structure. So you might find that a useful connection to the solid state stuff. I remember I was not comfortable with that my first time through solid state after Shankar; it wasn't until I had the same instructor explain perturbation theory and band structure to me that I got it.

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I would definitely recommend working your way through Dirac's 'The Principles of Quantum Mechanics'.

I had taken two or three courses on quantum theory a while ago and have read many books on the subject over the years, but I always had the impression that there was a kind of arbitrariness or lack of justification to some of the 'postulates' and a kind of 'magic' related to the applications of those postulates. Yes they give answers that agree with experiments, but what are the founding principles? Where do they come from?

Some examples:

  1. Why is the wave function complex?
  2. Where does $[\hat{q},\hat{p}]=i\hbar \hat{I}$ come from?
  3. What is the difference between the Schrodinger, momentum and Heisenberg representations. What is a representation for that matter and why use them?
  4. Can you derive Born's rule?
  5. Where does Dirac's delta function come from? etc. etc. Hundreds of questions like this...

So I worked through Dirac's book line by line.

And the book really is a work of genius. With very few assumptions (starting with the Principle of Superposition), Dirac builds up an entire architecture for quantum mechanics in a way that is understandable and generalizable. Yes, it's a slower read than Griffiths, Shankar, Levi, Binney et al. or Cohen-Tannoudji et. al (which are all superb). And of course there are no modern experiments described. But it will provide you with an extremely strong theoretical foundation with which you can try to understand quantum theory without getting completely bogged down in the mathematics. (Mathematicians might enjoy the less readable but perhaps more pedagogical 'Mathematical Foundations of Quantum Mechanics' by von Neumann).

There is no bibliography. None. Because everything is derived from a few assumptions. It is completely self-sufficient as a text.

And of course in his Nobel lecture ("The Development of the Space-Time View of Quantum Electrodynamics", Nobel Lecture, December 11, 1965), Richard Feynman credited Dirac's book. He said it inspired him to strive to develop new descriptions of the world which lead to his version of Quantum Field Theory.

[The answers to the above are all in the book! Very very briefly: 1) This follows from the Principle of Superposition; 2) From the assumptions that two observables $u$ and $v$ in quantum theory have a commutator related the classical Poisson bracket and that observables need to have real values (so need to be represented by self-adjoint operators); 3) A representation is just a way of describing abstract quantities like vectors, operators etc. in a simple way via a set of numbers (like coordinates relative to basis vectors in geometry). The Schrodinger representation is a description that focuses on position co-ordinates where states are time dependent, whereas in the Heisenberg representation states are stationary; 4) Yes. Dirac tells probabilities can be viewed as expectations of an indicator function(!); 5) It arises naturally when we describe orthogonal states in the case where observables can be continuous.]

So I would strongly recommend that anyone interested in Quantum Theory reads it. Even if it takes a while.

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