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Teaching myself QM

  1. Mar 17, 2007 #1
    I am trying to learn undergraduate-level quantum mechanics on my own. I would estimate my background to be that of a sophomore/junior year physics major.

    I have access to only the following books:
    • Introduction to the Quantum Theory - David Park
    • Quantum Mechanics - Eugen Merzbacher
    • Physical Chemistry - P.W. Atkins
    • Mathematics of Classical and Quantum Physics - Byron and Fuller
    • Third Volume of the Feynman lectures on physics

    I am not sure what is the best way to proceed. I don't have any specific problems with the materials at the moment, but I do have issues drawing up a path for myself.

    So does anyone have any suggestions on how I should approach self-studying QM? I realize that my request is a bit vague, but at the moment I am unsure of where to begin. If someone could give me a general path of study, I would appreciate it greatly.
     
  2. jcsd
  3. Mar 17, 2007 #2

    JasonRox

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    I would just say read the preface of each textbook. They tell you what to expect and what the pre-requisites to the textbook are. Then choose what textbook suites you and read from there.
     
  4. Mar 17, 2007 #3

    quasar987

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    Definately read from more than one textbook. Flip through each book to see which one you like best as far as style/format is concerned and take out all your favorite ones.
     
  5. Mar 18, 2007 #4
    I taught myself QM (from a math/comp sci background).

    I'd strongly recommend both Shankar books - "Basic Training in Mathematics" and "Principles of Quantum Mechanics" in that order.
     
  6. Mar 18, 2007 #5
    If I was to teach myself QM, I would first get a very solid understanding of classical mechanics.
     
  7. Mar 18, 2007 #6

    JasonRox

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    You know Quantum Mechanics?
     
  8. Mar 18, 2007 #7

    mjsd

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    well... true... eventually you may want to learn classical mechanics in good details for many of the ideas in QM are "borrowed" from CM.

    Quantum Mechanics - Eugen Merzbacher is a very good book.. but you do need to be strong in maths .. and it does get quite advanced towards the end... it is usually a higher year uni textbook
     
  9. Mar 18, 2007 #8
    Well, I know 2nd year QM and am currently learning 3rd year QM and infact using Eugen Merzbacher's book. Note that I actually haven't learnt a second course in CM and regret it but I have a professor teaching me so that makes things a bit easier.
     
    Last edited: Mar 18, 2007
  10. Mar 18, 2007 #9
    I have been working through Goldstein's Mechanics and Landau's Mechanics, doing the problems and such, so if, along the QM path, I get stuck, I can always take a break and go further in CM. I'm assuming that things like Lagrangians and Hamiltonians are the sort of prerequisites you are talking about.
    Would the Mathematics for Classical and Quantum Physics book serve the same purpose as "Basic Training in Mathematics"? I also forgot to mention that I have Boas and Arfken.

    People have recommended to me "Principles of Quantum Mechanics" many times, so would that be a worthy investment, or should I stick with what I have?
     
  11. Mar 18, 2007 #10
    I haven't used Boas, but I believe it'll contain similar material to "Basic Training". Arfken's at a higher level, so is Byron and Fuller (all this IMHO of course).

    I can't comment on Merzbacher, since I've never used it.

    Other supplimentary texts I used:
    Schaum's outline for QM and maticies
    Picture Book of QM, by Brandt, Dahmen - lots of cool graphs of the various quantum scenarios
    Practical Quantum Mechanics - Flugge - lots of worked out problems
    Greiner series on QM - found it cheap at a used book store. Lots of worked out examples
     
    Last edited: Mar 18, 2007
  12. Mar 18, 2007 #11
    This is good, because I have done everything in the Boas book.

    I'll try to stick with Merzbacher, because the Park book simplifies too much and explains too little. If I hit any math snags, I'll study from Arkfen and the Mathematics of Classical and Quantum Physics book.
     
  13. Mar 18, 2007 #12
    IMO there are two levels at which someone can study basic QM, depending on their math backround.

    Level 1: Backround includes a year of differential equations, a semester of linear algebra, and some study of the physics specific special functions (Legendre, Hermite, Laguerre) in Boas/Arfken.

    Level 2: Backround includes a year of Analysis, covering topics from functional analysis (real and complex analysis are not that important though) and a second, more abstract, course on linear algebra.

    Students from level 1 will gain a working knowledge of how to do computations in QM. You can solve the shrodinger equation for a variety of physical systems, work out calculations with spin operators, and learn basic perturbation theory.

    A knowledge of level one would allow you to read along with many journal articles and know the math behind the calculations of Energy levels, decay times, tunneling probabilities etc.

    Unfortunately, without a knowledge of level 2, the student cannot understand where QM comes from or I why any of its methods make sense! For this reason, I strongly suggest going directly to level 2.
     
  14. Mar 18, 2007 #13
    Do you advise, then, that I learn the mathematics behind level 2 first? Based on what you have said, I am prepared for level 1, but insufficiently prepared for level 2.
     
  15. Mar 18, 2007 #14

    marcusl

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    Goldstein is a graduate level text, so if you are having no problems with it then i think you'll do ok with Merzbacher which is one of the classic and popular grad level (usually) texts. I personally don't care for Merzbacher's style, but textbooks are personal and you just need one that suits your learning style as mentioned above. Griffiths and Shankar are widely used and liked for advanced undergrad QM.
     
  16. Mar 18, 2007 #15
    I'd just dive into the Park book, with Feynman as supplemental reading. Unless you've never seen a differential equation or a Fourier series before, I don't think you need to spend a lot of time on math background. Particularly the level of detail of Byron & Fuller, while interesting, is hardly necessary.
     
  17. Mar 18, 2007 #16
    I suggest you begin learning level 1. When you encounter derivations that are unsatisfying or even don't make sense you will be motivated to study the math needed for level 2.

    A good mathematical bridge between level 1 and level 2 is Sturm-Louiville theory. Sturm-Liouville theory is about the conditions under which a 2nd order ordinary linear differential equation will lead to set of solutions that can be used to approximate any function by an infinite series. An example is:

    y'' + (n^2) y = 0

    y(0) = y(pi) = 0


    Which has the solution set {Sin(nx), Cos(nx)} , which as you know from fourier series, can be used to approximate any function by an infinite series. Similarly with Legendre, Hermite, etc.
     
  18. Mar 25, 2007 #17
    Okay, I originally decided to go through Merzbacher, but I am getting confused too often. I can follow the mathematics, but I'm not sure what it is that I am doing while I am calculating. Although Merzbacher says in his preface that he doesn't expect any prior experience with QM, he skips so many little bits of critical information throughout the text that progress is slow.

    I am going to get the Shankar book, because I flipped through it and found that it fills in the gaps that Merzbacher ignores. So once I get it, I should be able to make better progress with QM.
     
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