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Quantum Mechanics Integral Trouble

  1. Feb 28, 2008 #1
    1. Problem: int[(x^2)*(sin^2 (n*Pi*x/a)] from 0 to a

    3. Physics teacher tells me to just look it up. I've wrestled with every table of integrals I can find (web, library, my books), but I'm still hung up.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 28, 2008 #2


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    Write it as x^2*sin(k*x) where k is n*pi/a. First use the trig identity sin^2(kx)=(1-cos(2kx))/2. Then to integrate something like x^2*cos(2kx) you just have to integrate by parts twice. It's not the easiest integral in the world, but it's not the hardest either.
  4. Feb 28, 2008 #3

    :biggrin: This has been vexing me for 3 1/2 weeks now! THANK YOU! :biggrin:
  5. Feb 28, 2008 #4


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