Tough integral

  1. This is actually part of a homework question for my Quantum Mechanics course but it is purely a math question.

    1 = A2[tex]\int[/tex]e-2(x/a)2sin2(kx)

    Note: for some reason the integral is showing up as a psi.

    where A, a, and k are constants and the integral is from -inf to inf (or 0 to inf with a constant 2 multiplying because the integrand is symmetric)

    What I am trying to do is solve for A. For the integral, there aren't any common forms that it matches up with that I am aware of. I've tried IBP but it seems to just get more and more complicated as it goes along. Any suggestions would be awesome.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. lanedance

    lanedance 3,307
    Homework Helper

    i'm gussing the limits are -inf to inf, this should help simplify things as
    [tex] \int_{-\infty}^{\infty} dx.e^{-x^2} = \sqrt{\pi}[/tex]

    I think a few IBPs is the right way to though it will be pretty messy
  4. Dick

    Dick 25,910
    Science Advisor
    Homework Helper

    Don't do parts. Use that sin(kx)=(exp(i*k*x)-exp(-i*k*x))/(2i). Expand everything and complete the squares. Then do a change of variables on each integral to convert everything to real integrals.
    Last edited: Oct 11, 2010
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