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Learning QM and the math required.

  1. Nov 14, 2006 #1
    I am trying to learn/relearn QM after a lengthy layoff (10+ years). I have had calc and diff EQ and partial Diff EQ but to be honest I don't remember the details anymore. For example I don't remember any of the standard solutions to integrals. I understand the principles but am just out of practice of actually doing it. I can follow along in a text ok but don't ask me to independantly solve the problems... the memory is just not there. I had actually taken a grad class or two on Quantum Chemistry so I know I could do it at one time!

    Here is the question. Is it possible to learn QM and QFT principles without the detail technical ability? I have access to text books but it would take forever to go back over them to bring myself back up to math speed. I am not looking to be a master on these subjects but I am trying to be able to understand grad level discussions. Thanks.

  2. jcsd
  3. Nov 14, 2006 #2
    First thing is to choose right books concentrating on physics and not in linear algebra or integrals, for example the green textbook by Dirac (foundations of qm or something?).

    For QFT, in my opinion, some mathematics are needed as it is very hard to find texts where things would be explained correctly without rigorous calucations.

    Anyways, physics is physics and math is math, so there is hope.
  4. Nov 15, 2006 #3


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    Nah, there's too much mathematics hidden in the axioms of QM (or QFT) that you can never say you fully understand them without understanding the maths.

  5. Nov 15, 2006 #4
    There aren't a whole lot of options. Most books that try to explain it without using math are not very good. The reason is because the concepts are largely mathematical, and do not translate well into plain English. So most mathless books tend to be general summaries of how the concepts have evolved over time (wasting space with what we used to think, rather than what is now thought), or try to explain the concepts with analogies that aren't really accurate, and don't give a real understanding.

    If you are really interested, though, I would recommend Penrose's book "The Road to Reality." It is over a thousand pages long, and is full of math. But he teaches you the math you need, as you go along. You'll be deep into imaginary/complex numbers before you know it. This book really was designed for people like yourself, and I think you might get a lot out of it. There are problems to solve, if you feel like it, but you don't have to in order to keep proceeding through the concepts. Just take a moment to ensure you understand what the equations are saying (and he does a good job of building up your understanding, step by step), and you'll get it.

    Hope this helps.
    Last edited: Nov 15, 2006
  6. Nov 15, 2006 #5
    I actually think I am somewhere in between the two worlds. It is not the general concepts of the math but the details. For example if a problem required integration by parts I could recognize that it was required but I would have to go look for the formula to do it. That is a trivial example but I think you get my point. It seem a waste to have to go back and relearn all the techniques to be able to understand the concepts the QM is about. No granted that I will have to learn some stuff like linear algebra (which I never go around to) but I expect that.
  7. Nov 15, 2006 #6
    I'm also trying to relearn QM after about the same layoff.

    It sounds like what you need is a book with lots of solved problems. There's a Schaum's outline on QM which get's middling reviews, but may be enough to get you started. I'm starting to work my way through Problems in Quantum Mechanics by Squires.

    I wouldn't worry too much about the math. It should start to come back as you work problems. Inability to remember arcane integrals should not be a problem; just get the Schaum's Mathematical Handbook and keep it handy.

    By the way, what text are you trying to learn from?
    Last edited: Nov 15, 2006
  8. Nov 15, 2006 #7
    I am using a "popular" book that has gotten poor reviews. It is by David McMahon. I think it got bad reviews because there are a million typo errors in it. I think it is making me look harder at each step in the solution. It does a pretty good job of explaining the steps but of course not perfect. I looked at Squires book but it doesn't look like there are any explanations. Is there or is it just a problems book.

    If you don't mind, what is your motivation for getting back into QM? Is your background (math wise) similar to mine?
  9. Nov 15, 2006 #8
    I've paged throught the McMahon in the bookstore. It looked like it was pretty much a condensation of the typical undergrad QM text.

    You've probably already found the errata on the author's website, though I don't know why there's only errata for 2 chapters.

    The Squires book has problems and complete solutions with a brief summary of the material at the beginning of each chapter, but only enough for reference while doing the problems. The value of a book like this is that you can check your work against the solutions, or peek if you get totally stuck.
    Last edited: Nov 15, 2006
  10. Nov 15, 2006 #9
    I wanted to learn some QFT, or at least QED, something I never got to in grad school. I found, though, that I'd forgotten a lot of QM, and probably never knew some of it very well (e.g. scattering theory). As for math background, I have 15-year old undergrad degrees in math and physics, with a few years of graduate physics courses (Goldstein, Jackson, and all that).
    Last edited: Nov 15, 2006
  11. Nov 15, 2006 #10
    Some other books that might be useful:

    Quantum Mechanics in Simple Matrix Form by Thomas F. Jordan. A cheap dover. I think this is probably the simplest book out there apart the typical pop-sci word salad books.

    Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles by Eisberg & Resnick. Does a good job with wave mechanics at an intermediate sophomore/junior level. Kinda pricey; look for it in the library or try to find a used copy.

    It looks like MacMahon relied a lot on the QM book by Griffiths, which seems to be well liked on this forum (too pricey for me, though).
  12. Nov 15, 2006 #11
    Anthony Zee's 'Quantum Field Theory in a nut Shell', is a very good book as he gives motivation for a lot of the mathematics. It will start you off well, from which you can move onto something a bit more concise, but highly recommended.
  13. Nov 15, 2006 #12
    I think if he's still struggling with introductory QM, Zee will just sit on the shelf for quite a long time.
  14. Nov 16, 2006 #13
    Below is an excerpt from the preface of Griffiths, which is one of the more popular upper-division undergrad QM books. The Eisberg & Resnick book mentioned above would be more elementary and less mathematical.

    Here's an older thread on this subject.

    Attached Files:

  15. Nov 16, 2006 #14
    The book I recommended in the second post is:
    P. A. M. Dirac: The Principles of Quantum Mechanics.

    It has lot's of physics and clear explanations why we use the mathematics we use. Bit expensive on amazon, but I would believe not so bad as used. As they say "Learn from the masters, not from apprentices."
    One good book focusing on the vector space side of QM is C. J. Isham's "Lectures on Quantum Theory: Mathematical and Structural Foundations". Paperback's cheap on amazon, very good for understanding, but doesn't teach you so much math.
  16. Nov 16, 2006 #15
    I was cheap and bought Schaum's Outlines Quantum Mechanics, and QM seemed hard.

    Then I bought Griffith's Intro to Quantum Mechanics, and QM seems easy.

    Schaum's is only good if you've already studied it and need to review before an exam - Griffith's textbook (for e&m also) is the proper way to go for truly learning the material.
  17. Nov 18, 2006 #16


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    I am teaching Quantum Mechanics at the undergraduate level and, given your background, I would hughly recommend (as others did) that you get Griffiths. It's an excellent book for self-study. People have also suggested Eisberg and Resnick which is an excellent complement at a slighlty more basic level but more extensive in the topics covered (includes some nuclear physics, atomic physics, particle physics, etc). Then Schaum and McMahon can be good to practice a bit. But you definitely should go through Griffiths (Shankar is also excellent).
  18. Nov 18, 2006 #17
    My choice would be Shankar. He wrote his book to be self-contained enough for self-study. And it's cheaper than Griffiths, which seems to have a rather inflated price. (Of course, if you have access to a good library, check them both out.)
  19. Nov 18, 2006 #18
  20. Nov 22, 2006 #19
    This looks interesting

    I just requested this book from my library; it looks interesting, may also do the trick. I'll post an update when it arrives:

    Author McMahon, David (David M.)
    Title Quantum mechanics demystified / David McMahon.

    Publication Info. New York : McGraw-Hill, c2006.

    Note "A self-teaching guide"--Cover.

    Claims to be just what you're looking for. More info at:
  21. Nov 22, 2006 #20
    That's the book the OP has, and which I suppose prompted his original post.
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