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Integral of this exponential

  1. Oct 22, 2014 #1
    Hey guys,

    if I have an integral of the form [itex]\int d^{3}x \hspace{2mm} e^{i(k\cdot x)}[/itex], how do I evaluate this?

    Thanks a bunch...
  2. jcsd
  3. Oct 22, 2014 #2


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    Staff: Mentor

    Is that d a constant, or the differential operator, or what?
  4. Oct 22, 2014 #3
    its the integration of measure, over 3 spatial dimensions
  5. Oct 23, 2014 #4
    How can you rewrite the exponential? Maybe try using Euler's formula if you aren't confident with the exponential.
  6. Oct 23, 2014 #5


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    Write [itex]{\bf k\cdot x}=kx\cos\theta[/itex]. Then do the angular integration.
  7. Oct 23, 2014 #6


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    Staff: Mentor

    Or in Cartesian coordinates, write out the dot product in terms of components: ##\vec k \cdot \vec x = k_x x + k_y y + k_z z##.
  8. Oct 23, 2014 #7

    Meir Achuz

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    [itex]\int d^{3}x \hspace{2mm} e^{i(k\cdot x)}=(2\pi)^3\delta({\bf r})[/itex], the Dirac delta function.
  9. Oct 23, 2014 #8
    Thank you Meir Achuz - that's what I was looking for :D thank you!!! Thanks everyone else for your help, I guess I should've specified that I was looking for it in terms of the Dirac delta.
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