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WKB theory? Pls help

  1. Nov 27, 2008 #1
    WKB theory?? Pls help

    1. The problem statement, all variables and given/known data
    WKB theory and WKB approximation. Are they same??

    2. Relevant equations
    I have to do a presentation about WKB theory in Physics (Quantum mechanics) but I dont know how to start from the WKB theory and come to WKB approximation. i.e. I don't find a direct connection. I know WKB theory is a method of solving differential equation but I do not know how to use it to solve any differential (well..2nd order) equation. It means I do not understand what WKB theory is (the basics) :( :(

    3. The attempt at a solution
    I tried to google and find the answer but did find a good explanation. I greatly appreciate if you can help me to understand this issue as this is vital to pass this course. Thanks.
  2. jcsd
  3. Nov 28, 2008 #2


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    Welcome to PF!

    Hi nukestrom! Welcome to PF! :smile:

    Googling is not a good phsycics research strategy.

    Wikipedia is usually helpful, so best to start there … if you can't find anything on PF first, of course :wink:.

    hmm … if you type "WKB theory" into wikipedia, you get the "WKB approximation" page …

    so I reckon they're the same! :biggrin:
  4. Nov 28, 2008 #3
    Re: Welcome to PF!

    Thanks for your reply. I greatly appreciate it.

    yes i did. I used wikipedia but their argument is not clear. They have proven it from few lines. As an example they have not explained "dominant balance" method which is essential to explain WKB. So wikipidea is good for expert but I want to learn basics.
  5. Nov 28, 2008 #4


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    Have you tried googling for

    "dominant balance" +WKB

    (with the quotes marks)?

    It should give you some google.books as well. :smile:

    And searching this forum for "dominant balance" (again with quotes) gave 6 hits.

    (I've never done WKB, so I'm afraid I can't help you any further.)
  6. Nov 28, 2008 #5
    Re: WKB theory?? Pls help

    The WKB method is also sometimes called the W.K.B. method, or WKBJ, or even Liouville-Green. All I know is that it is an asymptotic technique used to determine large eigenvalues for oscillation solutions of differential equations. Maybe this extra information helps when googling for information.
    Actually, I just looked it up in a PDE book by Haberman, and he refers to (after making implicit use of WKB) to Bender and Orszag (1999), Kevorkian and Cole (1996) and Nayfeh (2002), maybe your university library has these books.
  7. Nov 29, 2008 #6
    Re: WKB theory?? Pls help

    Its Ok. Thanks anyway
  8. Nov 29, 2008 #7
    Re: WKB theory?? Pls help

    Thanks for your info. Yes, I use Orszag and got an idea about Dominant Balance method. But the transition (WKB theory) from the mathematical concept to quantum mechanical aspects is still not clear.
    Thats the problem.

    Thanks again for your info.
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