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I am a first year PhD math student, and must decide: should I study Quantum Mechanics, although I don't have undergrad background in Physics?

Let me be more specific about my situation:

  1. Background:
    I'm a first year PhD math student with undergraduate background in Computer science. I switched from Computer Science to Math because I want to study Quantum Computing, in particular involving Quantum Mechanics.

    I only learned "general physics" (for non-physicists) in my undergraduate studies, and in particular didn't learn anything about Lagrangians or Hamiltonians, and very little about Maxwell's or Schrödinger's equations; and that was some time ago now besides.

    I also don't know anything about Partial Differential Equations, and am planning to review my Linear Algebra.

  2. Situation:
    My math department allows me to take one qualifying exam in Math and the other in another department (though the procedure is rather complicated.) I wish that I could take Quantum Physics as the second qualifying exam, but I should be extremely cautious about this decision. (To me, qual exams in my math department are really challenging, not to mention in another department). Now, I have to take some undergrad courses in math since I did not have math knowledge in undergrad, so if I take physics courses then the time to meet my math degree requirement has to last longer.

  3. Expectation:
    I want to study Quantum Information/Computing and in the long term to study Quantum Mechanics. I think the sooner I take the course Quantum Mechanics, the better I study Quantum Information/Computing, but I know everything is not as easy as I expect.

Do I need to prepare more before taking graduate Quantum Mechanics?

Your suggestion, experience will definitely help me to decide.

Urb
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Thang
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    Do not attempt to learn quantum mechanics or quantum computing without being very comfortable with linear algebra. You should be extremely comfortable with inner products, complex numbers, and eigenvalues to seriously study quantum computing; familiarity with Taylor series is also a big plus. Depending on just how much linear algebra you have to review, I would caution you to be very careful about making any commitment in the short term that you might find difficult to fulfil. – Niel de Beaudrap Jun 23 '12 at 16:53
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    These sorts of questions are very shoe-gazing--- stop worrying about background, you can look up all the unfamiliar terms with google. Just read a book and ask about the content you find confusing. You can read any book and learn basic QM in a few weeks. Dirac is self-contained, and so is Neilson and Chuang (but the latter is chatty). The Feynman lectures build up intuition quickly, and Polchinsky's string theory books has a fantastic path integral appendix. – Ron Maimon Jun 23 '12 at 18:58
  • Start by learning classical mechanics...... – Chris Gerig Jun 23 '12 at 20:50
  • Then electrodynamics.... Otherwise QM is just gonna be general nonsense like category theory to you. – Chris Gerig Jun 23 '12 at 20:51
  • Ron wrote: "You can read any book and learn basic QM in a few weeks."

    Not everyone is a Ron, Ron. :)

     – Alfred Centauri Jun 23 '12 at 21:08
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    @AlfredCentauri: I am just sick of these questions "Gee, I read this and this, can I read this and that now?" This is just procrastination, just read it and ask when something is confusing. I want to point out that it took me much more than a few weeks when I first learned it, it took several months, so that comment is not about me, personally (I am a very, very slow learner, I think). but nowadays the presentation has improved, and there are online resources, so it should go faster. – Ron Maimon Jun 24 '12 at 05:44
  • I agree on the Feynman. It definitely is one of the most accessible texts in physics. – Emilio Pisanty Jun 26 '12 at 11:22
  • Related: http://physics.stackexchange.com/q/38963/2451 and links therein. – Qmechanic May 28 '13 at 16:16

4 Answers4

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You may find my book Classical and quantum mechanics via Lie algebras useful. It doesn't assume any prior knowledge of physics (except at places where you can skip it without harm) and develops on the fly whatever is needed.

Urb
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Arnold Neumaier
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Do I need to prepare more before taking graduate Quantum Mechanics?

As an EE grad student, I once enrolled in the first of a graduate class series on QM. On the first day, the professor asked for a show of hands indicating what undergraduate courses on QM had been taken by the students in the class. He was surprised that I and another student had not taken any undergraduate QM classes so he asked to see us after class.

He was very cordial but frankly asked us to reconsider taking his class. He pulled out some of the early homework sets which were, he said, review. I recognized very little of it despite having casually studied some QM texts in years past.

So, after having given that preface, I'll give you my advice. Take an undergraduate class or three in QM to prepare for graduate QM.

Alfred Centauri
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  • When I took grad QM there were two chemistry students in the class who had taken pchem or whatever and knew what QM was, but didn't have any real background. They worked hard and eventually both aced the entire sequence. So one could, in fact, also just rise to the occasion instead of lowering their expectations of themselves. – wsc Jun 24 '12 at 15:02
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    It's quite odd that you seem to be inferring that making a rational decision to take a more sane approach to learning QM amounts to "lowering their expectations of themselves". Very odd indeed. – Alfred Centauri Jun 24 '12 at 15:06
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    I don't see why that's so odd. A lot of rationalized decisions in fact correspond to lowered expectations. Look, the original questioner wants to be a professional researcher in QInfo -- if you wanted that for yourself, you would've taken the grad class too. – wsc Jun 24 '12 at 15:11
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    A rational decision requires understanding the entire context of one's goals, one's time, one's experience etc. It's not about lowering one's expectation of one's self in this context. It's about asking the question "am I willing to pay the price?". In order for the two chem students to ace the class, they paid a price in terms of time and effort that, in the entire context of their goals, may or may not have been the most rational use that time and effort. – Alfred Centauri Jun 24 '12 at 15:34
  • Alright then, in those terms the advice you're giving is still dangerous because you're applying your own weights. If the questioner is sincere in his goals, he absolutely should be willing to pay any price. I was pointing out that graduate QM classes are not at all impossible for unprepared but hardworking students, where I read this answer as suggesting the opposite. – wsc Jun 24 '12 at 16:01
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    Again, that's very odd. Pay any price? Seriously? That's completely irrational. But, having said that, it's quite a stretch to interpret my advice as suggesting that it is impossible for an unprepared, hardworking student to do well starting out with a grad QM class. If his is sincere in his goals, including the stated one of "long-term study of QM", then he has the time and, in fact, owes it to himself to properly prepare himself for the grad QM class. – Alfred Centauri Jun 24 '12 at 16:42
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I would avoid the Feynman Lectures for QM. Griffiths is probably your best option. Newer editions have a nice appendix on Linear Algebra. It doesn't assume knowledge of partial differentials. Partial Differential Equations for Scientists and Engineers by Farlow is a great intro to PDEs.

MadScientist
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    Why would you avoid the Feynman lectures? I learned QM from Feynman and Dirac, and they were completely complementary. The Feynman lectures are perfectly clear and fine, and there is never a reason to tell people not to read something unless it is badly written or full of mistakes, which Feynman is most definitely not. – Ron Maimon Jun 23 '12 at 19:53
  • @RonMaimon: I was under the impression you only read from people who directly did the things they write about. – Nikolaj-K Jun 23 '12 at 21:36
  • @NickKidman: Feynman redid all the things he wrote about, to make sure he knew it as well as the original folks. This is the extra mile of good pedagogy, and it makes his presentations of elementary topics beyond reproach (and also self-sacrificing--- nobody gives you grant money to rediscover old stuff). Feynman made sure to do this, following history meticulously, redoing all the arguments from scratch. He starts the lectures with Democritus and Archimedes (the existence of atoms and potential energy) then moves on to Newton (momentum is conserved) and Laplace (virtual work). – Ron Maimon Jun 24 '12 at 05:39
  • @RonMaimon: I was more pointing at the statement "there is never a reason to tell people not to read something unless it is badly written or full of mistakes". Putting this together means every book not written by someone who invented something is badly written and full of mistakes. Of course, if you make it okay to also consider people who redid calculations, then the initial argument can never be checked as criteria. – Nikolaj-K Jun 24 '12 at 09:47
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    +1 for the Griffiths recommendation. The reviews on Amazon.com are very favourable and his electrodynamics books is great. – Physiks lover Jun 24 '12 at 14:30
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    @RonMaimon I didn't find his lectures on QM as helpful as his other lectures when I read it as an introduction for my QM course. He approaches it in an interesting way, but it is very odd. Does he even mention raising and lowering operators? Does he solve the Schrodinger Equation for all the standard simple systems? Looking at the contents, there doesn't seem to be much on perturbation techniques either. Griffiths covers much more and much more of what would be considered essential today in a breezy light style that really makes QM appear easy. – MadScientist Jun 24 '12 at 15:15
  • I wouldn't worry too much about studying classical mechanics in detail because QM is very different. I could easily imagine someone doing well in QM with only a little knowledge of classical mechanics. Then again, you can't really appreciate the oddness of QM without some knowledge of classical mechanics. – MadScientist Jun 24 '12 at 15:21
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    @RonMaimon And I'm only saying he probably shouldn't go there for an introduction to QM. There are better options. However, after reading some Griffiths, it could be beneficial. I'll put it this way: If you did an experiment where two people with nearly identical skill levels in physics were tested on QM and one read Griffiths and the other read Feynman, the student who read Griffths would probably do much better, in my opinion. But, learning is subjective and part of the fun of teaching yourself is picking out the book that suits your style. – MadScientist Jun 24 '12 at 15:30
  • Quantum Mechanics: Principles and Formalism (Dover Books on Physics) [Paperback] by Roy McWeeny is an inexpensive option that covers a lot of material very concisely. (It's about 150 pages) http://web.doverpublications.com/cgi-bin/toc.pl/048642829X – MadScientist Jun 24 '12 at 15:41
  • @BB1 I'd say Griffiths teaches you how to do QM without really teaching you how to think about QM. For your thought experiment, I hypothesize that the student who studies Griffiths will do better on exercises but the student who studies Feynman would write the better essay. :) Both are of course essential skills. – wsc Jun 24 '12 at 16:08
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    @wsc I wouldn't even agree with that. Griffiths is very clear about meaning. The first and last chapters cover that very well. – MadScientist Jun 24 '12 at 16:27
  • @BB1: Once you read Feynman and Dirac, you can read Griffiths too (quickly). The issue is that the ideas in Feynman include lattice Schrodinger equations, two-state and three-state systems, the solution to the H-atom, (but without justifying the exponential ansatz, something that is not done in Griffiths either. It comes from Schrodinger's experience with Fokker-Planck equations or from Pauli's algebraic solution). To learn Schrodinger's equation without learning lattice hopping models is no good--- it makes the effective mass of electrons in metals mysterious as well as conductivity. – Ron Maimon Jun 24 '12 at 17:40
  • @BB1: The reason he skips the "standard techniques" is that they are no good pedagogically. It seems that all people do in QM classes is solve the harmonic oscillator again and again, and this is stunting students into a stupor of triviality. Feynman would just give the quadratic path-integral, that's all it is. Why not solve some other exactly solvable systems? Why not present some nontrivial ground states? QM books are 10,000 presentations of Clebsch-Gordon coefficients and Spherical harmonics in the least illuminating ways. Gottfried's quantum mechanics book is a great one by the way. – Ron Maimon Jun 24 '12 at 17:43
  • Hm. I don't have Griffiths handy, and I can't remember what he says in the first and last chapters. I just remember the book being very mechanical and when I talk to undergrads who used it they often have really weird misconceptions even as they tear through the homework problems of, say, Shankar. But my favorite QM book is Gordon Baym's, so what do I know of all this? ;) – wsc Jun 24 '12 at 18:31
  • In the first chapter he presents the probability interpretation of the amplitude of the wave function and the idea that the wave function is what is being solved for. He does a great job of presenting the grand scheme of QM and I never felt like I was lost in the details. And I went away from the course thinking QM is easier than any other branch of physics. In the last chapter he presents Bell's Theorem and the philosophy of QM. Everything is presented very clearly and it is VERY easy. My personal strategy is to start with the easiest option.This is ultimately subjective isn't it? – MadScientist Jun 24 '12 at 19:19
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With a computer science background, you may appreciate the following "physics-free" introductions to quantum computing for computer scientists:

For a more in-depth introduction, the standard text is

This textbook also requires only a very limited physics background. The basic tool of theoretical quantum computing research is certainly linear algebra. Once you have covered the basics, I would also recommend some matrix analysis book, such as Horn & Johnson's.

Urb
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Martin Schwarz
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