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Integral of Complex exp of dot product

  1. May 23, 2010 #1
    [tex] S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx[/tex]

    How would one approach this integral?
    I tried to "ignore" the dot product and proceeded with [tex]exp(i\vec{q}\cdot \vec{x})=exp(iqx) [/tex] and got a wrong answer.
     
    Last edited: May 23, 2010
  2. jcsd
  3. May 23, 2010 #2
    If this integral is to be done in 3D, one may switch to spherical coordinates which has the volume element

    [tex] dV = r^2 sin(\theta)\; dr\; d\theta\; d\phi [/tex]

    and also, the dot product is

    [tex] |x||q|\; cos(\theta) [/tex]

    if x = r and play around with substitution, this integral might be easier to do.
     
  4. May 23, 2010 #3
    Thanks!
     
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