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Math Help - Delta function in 3D

  1. #1
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    Delta function in 3D

    Hi,I need to prove the following relation  \nabla^{2} = −4π\delta (R) where R=(x-y), x,y \in R^3  and  \nabla^{2} is taken over x_{i} and  \delta(R) is the 3D delta function (=1 iff x=y)Thanks!Isatis
    Last edited by isatis55; November 8th 2012 at 11:08 AM.
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  2. #2
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    Re: Delta function in 3D

    Hey isatis55.

    Can you please define specifically the definition of the 3D delta function given <x,y,z> in R^3 where you map <x,y,z> -> w?
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  3. #3
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    Re: Delta function in 3D

    Quote Originally Posted by chiro View Post
    Hey isatis55.

    Can you please define specifically the definition of the 3D delta function given <x,y,z> in R^3 where you map <x,y,z> -> w?
    3D delta functional with the usual abuse of notation, for any function on \mathbb{R}^3 continuous at \bf{0}:

    \delta(f) = \int_{\mathbb{R}^3} f({\bf{x}}) \delta({\bf{x}}) d{\bf{x}}=f({\bf{0})

    (the first and last terms above are the definition, the middle term is a common suggestive abuse of notation.)
    Last edited by zzephod; November 8th 2012 at 10:27 PM.
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