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The greatest of books?

  1. Nov 26, 2013 #1
    Hello there peers :smile: !
    I am an extremely curious fifteen year old boy and I must say that there's nothing more intriguing and superb to get curious about than quantum mechanics. Though don't get the wrong idea that I'm interested in the weirdness of it. Au contraire! Rather I'd consider myself to be "professionally" curious, i.e. I wan't the real deal and am not scared of the mathematics. Instead, I love the way we can communicate with nature in a sensible way through symbols on paper, that's why I entered the beautiful field of physics a few months ago starting to learn calculus and get on going with the overall ideas surrounding our understanding of nature's ways. Now I still have lots to learn in Partial Dequations (PDE) but that's not the point of me making this thread. I would kindly appreciate anyone who can share with me the title of what they consider to be the greatest of books on quantum mechanics, that is both comprehensible by the beginner in Q.M. and also introductory and beyond on the mathematical underlyings of Q.M. I guess you know by now that I love the math of it so no problems from that side. If you think the book is great and does its job well, then I'd be very grateful if you leave a reply below. And by the way you may as well suggest something on partial d's as well while you're on it.
    Thank you so much in advance. :approve:
  2. jcsd
  3. Nov 26, 2013 #2


    Staff: Mentor

  4. Nov 26, 2013 #3


    Staff: Mentor

    Assuming you are not scared of math I would start with Lenny Susskinds books (don't skip the Classical Mechanics one - its very important)

    Those books also have associated video lectures:

    Then Hughs - The Structure And Interpretation Of QM:

    I would also suggest Griffiths, but it is a bit pricey, so after that I like Quantum Mechanics Dymystified at a more reasonable price:

    Then you are ready for IMHO simply the best book on QM there is - Ballentine - QM - A Modern Development:

    It is THE book. Once you have mastered that, you are at graduate level in QM.

    But don't skip the sequence - each book I have suggested builds on the previous one.

    Last edited by a moderator: May 6, 2017
  5. Nov 27, 2013 #4
    Well, thank you kind people who replied. I'll definitely be picking up Griffiths book as I've heard some pretty good reviews for it and definitely check Leonardo's(inside joke) lectures on youtube.
  6. Nov 27, 2013 #5
    There are very little physics books which actually do justice to the math in QM. Most books kind of "butcher" it. Of course, this is no problem to me. Physicists are no slaves of mathematicians so they are not forced to do things with a mathematicians' rigor and carefulness. In fact, the mathematicial foundations of QM are so incredibly difficult that it would take a significant time to study all you need. Furthermore, they add not much to the physics, which I assume is what physicists are interested in. Still, you mention being very interested in the math behind QM, so I need to disappoint you and tell you that for a first time learning QM, you're not gonna see QM with the right mathematics foundations in your book.

    I would recommend you to study some linear algebra first, the book "Linear Algebra done wrong" is freely available and great: www.math.brown.edu/~treil/papers/LADW/book.pdf‎[/URL]
    Lang's book is also nice: [url]https://www.amazon.com/Introduction-Linear-Algebra-Undergraduate-Mathematics/dp/0387962050[/url]
    Be sure to get well acquainted to dual spaces and inner product, then QM will make waay more sense.

    I recommend against Griffiths, I think the book is horrible. I agree with bhobba that Ballentine is probably the best book you can find on QM (and one of the most math-oriented, even though it's not completely rigorous). Then again, Ballentine is a bit advanced. For a first encounter with QM, I think [URL]https://www.amazon.com/Quantum-Mechanics-Applications-Nouredine-Zettili/dp/0470026790[/URL] Zettili is your best bet. It's an awesome book with great exercises.

    You do know a bit of classical mechanics already, no? If not, you should study that and at least get acquainted with the hamiltonian formalism. The book by Susskind linked by bhobba is great, try to read to that first.
    Last edited by a moderator: May 6, 2017
  7. Nov 27, 2013 #6


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    Learn classical mechanics and electromagnetism first.
  8. Nov 27, 2013 #7
    I agree with this, at minimum with respect to classical mechanics. Classical mechanics is still a more appropriate avenue to learn about many mechanical (among other) concepts such as momentum, velocity, kinetic energy, etc which remain central in quantum mechanics.

    That being said, if you really want to run with with quantum mechanics then Griffiths and/or Zettili are great choices. Griffiths is very insightful but very basic. Zettili is a tad bit more mature. The main advantage of Zettili is that each chapter has a large selection of worked problems (mostly computational ones - which is good so one can see how one does calculations in quantum mechanics without having to deal with all the tediousness oneself).
  9. Nov 27, 2013 #8

    George Jones

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    I think Zettili's strength is also its weakness:
  10. Nov 27, 2013 #9
    Last edited by a moderator: May 6, 2017
  11. Nov 27, 2013 #10


    Staff: Mentor

    Even though its the book I learned QM from, and the above is true without question, it lags far behind modern treatments like Ballentine in explaining exactly whats going on. For example Ballentine fairly rigorously develops Schrodengers equation from symmetries, Dirac from vague analogies to Poisson Brackets.

  12. Nov 27, 2013 #11


    Staff: Mentor


    But I hasten to add that anyone with an exposure to Hilbert spaces, which many study undergad, can understand the mathematically rigorous - Mathematical Foundations of QM by Von Neumann.

    I just don't want the OP to get the impression a mathematically correct treatment is so difficult its beyond reach.

    A note to the OP - until you understand things like Hilbert Spaces it best to stay away from mathematically correct books like Von Neumann

  13. Nov 27, 2013 #12


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    Ballentine doesn't teach you how to do QM. OP, your choice to get Griffiths is probably the best one.
  14. Nov 28, 2013 #13
    I am understanding something now from reading through all your guys' responses: Learning ways are entirely subjective, thus the many different book suggestions from all of you. It's ok though, I'll go with Griffith's first and see for myself. My favorite way of studying is to hear/read from many perspectives and in the end make up my own, so no problem. Thank you so much everybody :D
    And by the way,
    I have studied linear algebra, vector analysis, state-vector spaces(that's what I call phase spaces) and have developed quite a nice understanding of what the inner product implies physically, not only mathematically. I LOVE VECTORS SO MUCH! And may I say the ket and the bra are the cutest little things in all mathematics?
  15. Nov 28, 2013 #14
    Oh sorry i forgot to ask: Has anybody gone through "The Road to Reality" by Roger Penrose? If so what did you think of it?
  16. Nov 28, 2013 #15
    I would say they're not part of mathematics to begin with. Only physicists use the notation. Mathematicians tend to hate it :tongue:

    It's more of a popsci book (a very very rigorous popsci book). It's a nice book to give you some intuition on the subject, but it's not good at all to use it to learn physics and math properly.
  17. Nov 28, 2013 #16


    Staff: Mentor

    My feeling is it will be overwhelming of the casual reader but for a recent undergrad physics major they would be able to plow through it without too much difficulty.
  18. Nov 28, 2013 #17
    The ket and the bra are definitely mathematical symbols used in a mathematical way. To say they don't belong in mathematics is kind of not the smartest thing because everything you can do with them falls into the realm of math. Except a very interesting idea I have of a t-shirt but not now...
    And I couldn't agree more on the book. It feels very ambiguous when you go through it, just doesn't feel right. Probably because it was made for the public, but it throws math down the readers' throat in every page. My mistake I bought it thinking of it as a rigorous book.
  19. Nov 28, 2013 #18
    I'm just saying that mathematicians very rarely use braket notation and prefer other notations which they find easier. Physicists prefer braket notations over the mathematician's notations. If you read a math book, then you will almost never encounter braket notation, you'll only see it in physics books or papers. So in that way, they are more about physics than about math.

    Not saying that a good mathematician shouldn't use braket notation. But it turns out that few actually use it consistently for some reason.
  20. Nov 28, 2013 #19
    I wasn't arguing about whether mathematicians use brackets or not I was just saying that the bra ket notation is mathematical, otherwise we wouldn't use it to describe nature.
  21. Nov 28, 2013 #20


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    Anyways, this is getting off-topic. Check out Griffiths and see how much you like it. Good luck!
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