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Expected values in infinite square well

  1. Dec 19, 2012 #1
    Ok...this must sound stupid, because i didn't found answer on the web and on my books...but i am having trouble with the infinite square well.
    I want to calculate <x>.
    V(x)=0 for 0<=x<=a
    <x>=\frac{2}{a}\int^{a}_{0} x \sin^2(\frac{n\pi}{a}x)dx
    Doing integration by parts i got to:
    What i am doing wrong?
    Thank you
  2. jcsd
  3. Dec 19, 2012 #2


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    Staff: Mentor

    I would expect an error in your integration, as the first expression is not zero and the following one is.
    Last edited: Dec 19, 2012
  4. Dec 19, 2012 #3


    look up
    \int u \sin^2(u)du
    in a Table of Integrals to find
  5. Dec 19, 2012 #4
    Yeah, i got it...it is easier to use table of integrals.
    it gives the expected [itex]<x>=\frac{a}{2}[/itex] for any value of n.
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