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Best way to learn QM comprehensively

  1. May 17, 2012 #1
    I want to go about learning quantum mechanics in a way that I can learn it in detail eventually.
    And I was wondering if someone could give me some advice or advice for how they learn't it,
    should I start learning calculus and the mathematics needed for understanding
    it or get one of these books that were recommended on a thread on this forum such as
    introduction to quantum mechanics by Griffiths or quantum reality: theory and philosophy by Allday.
    Any pointers?
    The main question is, learn the mathematics first or get a book that will cover it in it?
     
  2. jcsd
  3. May 17, 2012 #2
    It depends on your current mathematical knowledge; if you don't know calculus yet, then definitely get the hang of that first. It would help if you specify your math knowledge so far.
     
  4. May 17, 2012 #3
    I am at the end of my maths GCSE, so I only know very basic trigonometry, quadratics.
    Thats about it.
     
  5. May 17, 2012 #4
    You need the mathematics before you even attempt it. Unless you are just interested in reading popular interpretations and such.
     
  6. May 17, 2012 #5
    Take further maths in A-level. After school, it gave me enough to start working at a snail's pace on a QM text, but, of course, even all the further math stuff soon runs out in a QM text and you will need good courses in multivariable calculus, linear algebra and differential equations to get a good grip on most of the stuff.
     
  7. May 17, 2012 #6
    Don't even think about attempting to understand QM in all its rigour. When I read your first post, I thought you were a first-year undergrad, but now given your background I'd say there's only a one in a million chance that you will even understand half of QM properly given your mathematical background.

    Students take years to familiarise themselves with linear algebra, differential equations, vector calculus and multivariable calculus. It cannot be done in a few weeks. It will take at least a couple of months. And then you will need to have a sufficient bakcground of classical mechanics because the standard way to introduce QM to students is through their understanding of classical mechanics. You can of course find resources that do not use this approach, but no matter what textbook, the authors assume that the student is an undergrad and they use reasonably complicated and perplexing terminology and generalisations, so it can get confusing.

    That's unless you just want a general picture of QM, which is perfectly possible given your level of mathematical background.
     
  8. May 17, 2012 #7
    Don't even think about this because I don't think that anyone really understands QM.

    Most undergraduate courses focus on giving you enough understanding of QM so that you can solve practical problems. That will take you about two to three years from where you are.

    One book I recommend is the classic French and Taylor. The reason I like it is that it's a stepping stone between "popular" accounts of QM and the "deep mathematical" parts.
     
  9. May 18, 2012 #8
    That is the sort of book I was looking for, how does it compare to something
    like griffiths, or are they for different sorts of purposes?
     
  10. May 18, 2012 #9
    It's more basic than Griffiths. Some people think "too easy" but it's something that's a stepping stone to Griffiths.

    Also

    http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2006/ [Broken]
     
    Last edited by a moderator: May 6, 2017
  11. May 18, 2012 #10
    Thanks for the help, I will get on with ordering it from amazon!
     
  12. May 19, 2012 #11
    I suppose this does beg the question, at my level is it possible to teach myself QM beyond popular interpretations?
     
  13. May 19, 2012 #12

    Fredrik

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    It's possible, but it won't be easy.
     
  14. May 19, 2012 #13
    I suppose though if I do learn these sort of things now, it *should* make things easier later on, or it will just cause me to fail my GCSEs and A-levels :biggrin:
     
  15. May 19, 2012 #14
    MIT's 18.01 course *seems* to cover all the calculus parts of C1-C4 in the A-Level maths syllabus. You could start off with that and move your way up. Learn the chapters that come before calculus from your A-Level textbook and then use 18.01 from OCW. I'd have done just that, had I known about OCW then! When you finish, 18.01, do 18.02 and then start doing some physics from 8.01 and 8.02. Actually, you might be able to start right after 18.01. Also, 8.01 might help you for your mechanics modules.

    Note that I haven't actually checked the syllabus word-for-word and it seemed to closely match what I did with CIE (my A-Level board) all the way up to differential equations. The above is more for your own personal study (suggested course of action - I may be wrong/you can disagree with me) and should not replace what you do in your A-Level classes at school! Focus on doing well on those, for you will need excellent grades (although A*AA-AAB will be fine, depending on where you're applying) to get into a good physics undergrad program in the UK.
     
  16. May 19, 2012 #15
    I have not started maths A-level yet, that will be at the end of 2013 when I start it as I am in year 10 now.
    In year 11 I am doing a AQA FSMQ, which is mean't to be a bridge to A level maths.
     
  17. May 19, 2012 #16
    Well, you'll have to go through A-Level maths, or part of it at least, before you're able to learn some physics. A-Level physics is just algebra based stuff...

    Hmm. I believe I did something similar when I did O-Levels - it was called "Additional Mathematics" and covered most of C1-C2. (or P1 for CIE)
     
  18. May 19, 2012 #17
    Do not touch griffiths.
    EVER

    Step 1. Maths - M Boas, Mathematical Methods in the Physical Sciences, learn the calculus in that book
    Step 2. Check out Landau and Lifgarbagez non relitivistic QM book (the first third of it at least)

    You'll know where to go from there!

    Good luck OP :biggrin:
     
  19. May 19, 2012 #18
    This is what I was looking for, you have made my day.
    I will get on with ordering that maths book!
     
    Last edited by a moderator: May 19, 2012
  20. May 19, 2012 #19
    I strongly disagree with this advice. Boas presumes university level calculus 1, or at least maturity at that level, and Landau doesn't have the 'fun' and explanatory prose that Griffiths has, and, it's more formal. I did first three chapters of Griffiths in high school and I don't think I could have put up with any other QM text for long back then. For a good basic understanding, all it requires is A-level calculus and a good chapter on vector spaces from an "additional math" kind of high-school book. Whereas both Boas and Landau are gems, I think they are inappropriate for a school kid; post freshman year at university, they are your friends.
     
  21. May 19, 2012 #20
    I wouldn't say university level calculus, there's no prerequisite for Boas that you couldn't lean via say Khan Academy in a few days.
    L&L certainly don't have a traditional 'fun' but there's certainly an unconventional fun in there and I'd say their explainations are better than Griffiths', especially when relating to the mathematical side of things (especially ladder operators, Griffiths mangles the whole concept into something only understandable if you learn about it somewhere else then completely ignore anything Griffiths has to say about them imo). I do agree that Boas and L&L may be hard for him but if he puts effort into it and does the problems he'll have no problem with it.
     
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