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Delta function

  1. Dec 4, 2013 #1
    My book loves to represent the delta function as:

    δ(r-r')=∫-∞exp(i(r-r')k)dk

    Now I can understand this formula if the integration was over the unit circle since. But this is an integration for which the antiderivative as no meaningful limit as x->±∞
     
  2. jcsd
  3. Dec 4, 2013 #2

    pwsnafu

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    The integral written is only true as formality. What's really going on is that Dirac is a tempered distribution, and hence has a Fourier transform. It can be shown that ##\hat\delta = 1##. What the equation is trying to say is that the Inverse Fourier of the constant 1 is Dirac delta.
     
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