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How do you integrate this function (not by parts)?

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data

    integrate: r2*exp(i*k*r - r2/a2) from -infinity to +infinity (in terms of r)

    2. Relevant equations

    relevant integration table

    3. The attempt at a solution

    not sure what this function or the method to solve this function is called
     
    Last edited: Oct 6, 2011
  2. jcsd
  3. Oct 6, 2011 #2

    Mute

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    I would start by completing the square in the exponential, and then changing variables to y = r - b, where b is whatever you get when you complete the square. Then, use know results for the integrals of Gaussian functions.
     
  4. Oct 6, 2011 #3

    CompuChip

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    Without going through the whole exercise, the thing that comes to mind is splitting off a square. I think that eventually you will find a substitution like [itex]z = r/a - \tfrac12 i a k [/itex] which will allow you to write it in terms of integrals like
    [itex]\int e^{z^2}[/itex] and [itex]\int z e^{z^2}[/itex]
    which you can do without partial integration.
     
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