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Delta function

  1. Dec 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that
    ##\frac{1}{\pi}\lim_{\epsilon \to 0^+}\frac{\epsilon}{\epsilon^2+k^2}##
    is representation of delta function.


    2. Relevant equations
    ##\delta(x)=\frac{1}{2 \pi}\int^{\infty}_{-\infty}dke^{ikx}##



    3. The attempt at a solution

    ##\int^{\infty}_{-\infty}\frac{\epsilon}{\epsilon^2+k^2}dk=\pi##
    One can take ##F[e^{-\epsilon x}]## and then put ##\epsilon to go to zero +. Why ##0^+##. I'm confused?
     
  2. jcsd
  3. Dec 20, 2013 #2

    Simon Bridge

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    What happens when you take the limit from the other side?
     
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