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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 other 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. Thank you.

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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
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
@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 5:44
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5 Answers

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.

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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
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
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
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
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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Not to be rude, but how are you a math graduate student - and don't know anything about partial differential equations?

If you want to studying QC, you have to learn a good amount of physics. Its up to you whether you do that via your own study of texts, or by classes. It sounds like you're quite behind on your math, so you'll have to do the same thing there. Keep in mind, there's nothing wrong with taking a few extra years in your graduate program (in fact, thats a good way to get a job after).

Get a copy of The Feynman Lectures. That should be plenty to prep you for a graduate physics courses, if you catch up on the math.

Consider getting a copy of the textbooks for relevant graduate classes (e.g. quantum mechanics, advanced linear algebra, group theory, etc).

Most importantly, don't let a weak background stop or slow you down.

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Mathematicians have different standards for knowing something. Partial differential equations means "viscosity solutions", "Sobolev metrics", "geometric flows", and all sorts of stuff that should make every physicist say "I don't know anything about partial differential equations". At least, that's what I say to myself. –  Ron Maimon Jun 23 '12 at 18:56
Furthermore, from the fact that the OP has a background in computer science, his mathematical background is almost certainly dominated by Discrete Mathematics, e.g. number theory. He probably knows some calculus, but to assume that "graduate math = multivariate calculus etc." is to take a somewhat narrow view of what mathematics is. –  Niel de Beaudrap Jun 24 '12 at 21:12
@NieldeBeaudrap my comment explicitly prefaced 'being a math grad' (i.e. regardless of background). The math/science graduate programs I am familiar with require a broad understanding of all basic material---which for math, I would assume includes basic PDEs. To assume that 'discrete math = broad understanding of the basics' is an extremely narrow view of what a graduate program tends to be. –  zhermes Jun 25 '12 at 0:44
@zhermes: I can speak from experience that past a certain point even of my Bachelor's studies, whether I could carry out any analysis of differential equations was completely irrelevant. (That my PhD thesis was in Combinatorics may have helped.) This is precisely how one may come to be a "math grad" without knowing much about PDEs. I never claimed that one may have "a broad view" of math without them, but I would suggest that you take a moment to recognise that there is a discrepancy between your notion of the necessary conditions to be a math grad, and the sufficient conditions in reality. –  Niel de Beaudrap Jun 25 '12 at 15:42
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You may find my book Classical and quantum mechanics via Lie algebras http://lanl.arxiv.org/pdf/0810.1019v2.pdf 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.

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your paper is amazing :D :D thanks .. i am a physicist and this is really worth looking at . –  Jose Javier Garcia Jun 24 '12 at 12:14
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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.

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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
+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
@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
@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
@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
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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 text book also requires only 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.

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protected by Qmechanic May 28 '13 at 16:10

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