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Spherical Co-Ordinate Integral

  • Thread starter Ayame17
  • Start date
1. Homework Statement

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!
 

CompuChip

Science Advisor
Homework Helper
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Try substituting x = cos theta (this is a common trick in theoretical physics, so remember it!)
 
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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