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Jacobian in delta function

  1. Dec 14, 2008 #1
    when using delta function [tex]\delta(r)[/tex] in cordinates othe then cartesian when does it needs to be divided by the jacobian for example in spherical coordinates

    [tex]\delta(x)=\frac{1}{r^2sin(\vartheta)}\delta(r-r_{0})\delta(\vartheta-\vartheta_{0})\delta(\phi-\phi_{0})[/tex]
    but if you want a delta function that involves only the radial coordinate doy you still need to divide all the jacobian like this [tex]\delta(r)=\frac{1}{r^2sin(\vartheta)}\delta(r-r_{0})[/tex]
    or only the radial part like this
    [tex]\delta(r)=\frac{1}{r^2}\delta(r-r_{0})[/tex]
    thanks
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  2. jcsd
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