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Normalization of a wave function with cosine

  1. Oct 21, 2007 #1
    I need to normalize the following wave function:

    psi= Cexp(-abs(x))exp(-iwt)cos(pix)

    I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is

    Psi^2=C^2exp(-2abs(x))cos^2(pix)

    Which seems like a fairly complicated integral to compute. I'm thinking that there is something that I'm missing about this particular wave function that will make it easier to integrate?

    Any help?

    Cheers,
    wakko =)
     
  2. jcsd
  3. Oct 21, 2007 #2

    Dick

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    Split it into x>0 and x<0 parts. For the positive part drop the abs. The negative part is the same since the integrand is even.
     
  4. Oct 21, 2007 #3
    That's not really the problem I'm having...I understand that I can double the integral over 0 to infinity, I'm just wondering if there is a simpler way to to figure out the integral itself.

    Thanks anyway.
     
  5. Oct 21, 2007 #4

    Dick

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    cos(pi*x)=(exp(i*pi*x)+exp(-i*pi*x))/2. If you do it that way you can turn the whole thing into one big exponential. Otherwise you can integrate by parts. It IS a somewhat complicated integral to compute. But not the worst.
     
  6. Oct 21, 2007 #5
    but if I do the conversion, I end up with an integrand that has i still in it, don't I? that doesn't seem right to me....
     
  7. Oct 22, 2007 #6

    Dick

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    It will seem right when all of the i's cancel in the end.
     
  8. Oct 22, 2007 #7

    clem

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    It's a bit easier to use cos x=Re[exp(ix)]
     
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