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B Is this QM learning pathway sound?

  1. Apr 18, 2016 #1
    just for personal enrichment I going to do a second reading of QM. my first was 20+ years ago and found the topic interesting. my education was exclusive to position space and solving problem after problem using SWE with a bazillion different boundary conditions and Hamiltonians, my calculus is OK.

    that's was all great but when I see something involving mixed states, density matrices, Dirac notation, quantum logic I don't even recognise it as QM and have no clue what is being described or discussed or what problem is being solved.

    plan;

    - do a course in mathematical/symbolic logic
    - do a course in linear algebra
    - do a course in abstract algebra eg group theory
    - jump into Ballantine textbook

    is this efficient?
    what would educators here recommend as a learning pathway.

    note this is just for fun and personal enrichment as stated.
     
    Last edited: Apr 18, 2016
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  3. Apr 18, 2016 #2

    atyy

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  4. Apr 18, 2016 #3

    dextercioby

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    Atyy is the only user of PF bashing Ballentine's research work and his textbook (which, by the way, honorably promotes T.F. Jordan's work on the Galilei algebra and its brilliant derivation of quantum mechanics - T.F.Jordan's own book is quite rare in univ. libraries), mainly because Ballentine [by his so-called "ensemble enterpretation of QM"] dismisses any form of (subjective) state vector collapse/reduction à la von Neumann (for example).

    I would advise the OP to stay out of the pest of quantum logic. If he wants to learn no functional analysis to grasp QM from a textbook such as Galindo and Pascual or A. Capri, then, by sticking to formal calculus, Weinberg's new book or the old one by Landau and Lifschits are still the best for me. I sense Sakurai's text is too much for you, right now.
     
  5. Apr 18, 2016 #4
  6. Apr 18, 2016 #5
    these books look relevant to my quest - extremely cheap. cant look inside tho. anyone read them?

    upload_2016-4-19_10-45-29.png
     
  7. Apr 19, 2016 #6

    A. Neumaier

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    The first few chapters of my free online book on classical and quantum mechanics may be useful side reading while you update your linear algebra. You get a simple and efficient introduction to quantum mechanics in the density operator form, closely paralleling classical mechanics.
     
  8. Apr 19, 2016 #7
    Thanks for making that available. Looks like a big job right there.
     
  9. Apr 19, 2016 #8
    Weinberg is great in showing the fundamental importance of symmetry in modern day physics.
    I don't really agree with his choice to use different notation, he doesn't like Dirac notation. (This is my opinion, probably biased by the fact that I learned the basics using exactly Dirac notation but the lecturer seemed to share that sentiment.)

    It is not for a first course as you suspected although it should be useful when you have been through the basics again.

    My experience with QM went something like Griffiths -> Basdevant/Dalibard -> Weinberg (-> Lecture notes by a mathematical physicist focused on many body QM).
    The first book was great for the place it occupied in our curriculum, we got our first quantum course in the third semester of the first year.
    It isn't that good in terms of subtleties and general ideas. But it helped me (mainly) by introducing some examples of quantum systems (Harmonic oscillator, potential wells, hydrogenlike atoms, ...).
     
  10. Apr 19, 2016 #9

    Demystifier

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    I strongly disagree. 99% of his book is the standard theory, and this standard theory is written better than in most (if not all) other books. I agree that Ballentine is mistaken in some parts (say 1% of the book), but that's not sufficient to dismiss the book as a whole.
     
  11. Apr 19, 2016 #10

    atyy

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    The 1% is when all text is uniformly weighted. But if one weights it by how fundamental the content is, and the fact that the error it is not just the occasional careless mistake (eg. Weinberg's error on the cluster decomposition is probably just sloppiness, not a deep misunderstanding on his part; similarly Feynman's error about Gauss's law is an incidental error, not due to Feynman having a deep misunderstanding of Maxwell's equations), then opinions about Ballentine can differ.
     
  12. Apr 19, 2016 #11

    Demystifier

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    Where (book title and page number) did Feynman make this mistake?
     
  13. Apr 19, 2016 #12

    Demystifier

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    I agree that the Ballentine's misconception is very fundamental. But still, given that many aspects of QM became clear to me only after reading Ballentine, my overall opinion of that book remains very high.
     
    Last edited: Apr 19, 2016
  14. Apr 19, 2016 #13

    atyy

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    It's in his original lectures, which are absolutely magnificent. Maybe I'm being harsh on Ballentine - but if one wants to read that stuff, may I recommend Peres's book instead. Peres is probably confused about the issue too, but his book is so gracefully written, I'm inclined to forgive him.

    http://www.feynmanlectures.caltech.edu/II_05.html
    "The same arguments can be used to show that no static distribution of charges inside a closed grounded conductor can produce any fields outside. Shielding works both ways!"

    http://www.feynmanlectures.info/flp_errata.html (Thorne's commentary)
    This second error was pointed out to Feynman by a number of readers, including Beulah Elizabeth Cox, a student at The College of William and Mary, who had relied on Feynman’s erroneous passage in an exam. To Ms. Cox, Feynman wrote in 1975,[1] “Your instructor was right not to give you any points, for your answer was wrong, as he demonstrated using Gauss’s law. You should, in science, believe logic and arguments, carefully drawn, and not authorities. You also read the book correctly and understood it. I made a mistake, so the book is wrong. I probably was thinking of a grounded conducting sphere, or else of the fact that moving the charges around in different places inside does not affect things on the outside. I am not sure how I did it, but I goofed. And you goofed, too, for believing me.”
     
  15. Apr 19, 2016 #14

    PeroK

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    I'm not sure why you'd need symbolic logic or significant abstract algebra to get stuck into QM. Calculus, differential equations and linear algebra for sure.
    I come from a pure maths background and have been learning physics since I retired a couple of years ago. I've found that generally being "fleet of foot" with mathematics is more important than being able to grind out formal proofs.

    Apart from learning about Linear Operators on Hilbert Spaces, I'd go easy on the abstract stuff.
     
  16. Apr 19, 2016 #15

    kith

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    If you feel like you still have a reasonable grasp of this material, I would recommend Sakurai's "Modern Quantum Mechanics". He starts directly with the most elementary quantum mechanical situation namely, that of a two-state system. Also he directly starts with the abstract formalism and later on derives wave mechanics from this. He has a lot of physical insights and doesn't overemphasize the mathematics. In addition, I would recommend linear algebra in some form (I agree with Pero that the rest of your suggested math courses won't help you much).

    I also like Ballentine. Like Sakurai, he has quite a few insights and treatments which you won't find anywhere else, and he goes even more in-depth than Sakurai. His chapter on the interpretation of QM is controversial (as you can see in this thread) but I don't view this as problematic. Mastering the formalism is much more important than thinking about the interpretation in the beginning. Just keep in mind that to take his words in the corresponding chapter with a grain of salt and you can return to the interpretation later on. In fact, many physicist don't care much about the interpretation.

    Both Sakurai and Ballentine are very in-depth (and therefore count as grad level texts). They do start with the basics but you have to check whether they are too dense for you or not. I cannot comment on more elementary books like Griffiths or Shankar because I don't have experience with them.
     
    Last edited: Apr 19, 2016
  17. Apr 19, 2016 #16

    kith

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    Independent of which book you chose for actually learning QM, you can also use Süsskind's "Theoretical Minimum" book on QM as a supplement. He aims at laymen who don't want pop science but the real deal. With this book, you won't lose track of the important ideas because of too much mathematical details.
     
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