Delta function

  • Thread starter aaaa202
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  • #1
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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->±∞
 

Answers and Replies

  • #2
pwsnafu
Science Advisor
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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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