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Spherical Co-Ordinate Integral

  1. Mar 24, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm trying to integrate the following:

    [tex]\int_0^{2\pi} \int_0^\pi \int_0^r \frac{m^2r}{4\pi} e^{-r(m+iqcos\theta)} sin\theta dr d\theta d\phi [/tex]


    3. The attempt at a solution

    Well, the question wasn't just that, my attempt was to get this far!

    I know that [tex] \int_0^{2\pi} d\phi [/tex] can just sit off to one side to be put in later, since there is no [tex]\phi[/tex] in the equation. Trying to do the next integral in, however, has proved difficult. I'd have to use integration by parts, since [tex]\theta[/tex] appears twice, but since I have an exponential and [tex]sin\theta[/tex] will just go around to [tex]cos\theta[/tex] and back again, I don't see how it will work. Any help will be appreciated!
     
  2. jcsd
  3. Mar 24, 2009 #2

    CompuChip

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    Homework Helper

    Try substituting x = cos theta (this is a common trick in theoretical physics, so remember it!)
     
  4. Mar 27, 2009 #3
    I've had a play around with that and, although it gives quite a nice number, I know the answer I need but can't seem to reach it...I've been told that I should get:

    [tex]F(q^{2})=\frac{m^2}{m^2+q^2}[/tex]

    The problem being, my integral still has an exponential factor - I'm not sure how to make it disappear!
     
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