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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
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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
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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 5:44
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5 Answers

up vote 3 down vote

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
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@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
up vote 1 down vote

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
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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up vote 1 down vote

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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up vote 0 down vote

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
@RonMaimon: I was under the impression you only read from people who directly did the things they write about. – Nick Kidman 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 5:39
@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. – Nick Kidman Jun 24 '12 at 9:47
+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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up vote 0 down vote

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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