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Diract delta function

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Justify the following expretion, in spherical coordinates;

    delta (vector r) = (1 / r^2 * sin (theta) ) * delta(r) * delta(theta) * delta(phi)


    2. Relevant equations



    3. The attempt at a solution

    I dont know what it means.... please help?
     
  2. jcsd
  3. Mar 11, 2009 #2

    lanedance

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    Homework Helper

    are you sure you don't mean
    [tex]
    r^2{\sin{\theta}.dr.d\theta.d\phi
    [/tex]

    this an expression for a volume integrand, over spherical coordinates [tex](r, \theta, \phi)[/tex]

    the delta represents each coordinate integral, whilst the [tex]r^2\sin{\theta}[/tex] factor comes from the jacobian, based on the coordinate transform from cartesian to spherical coordinates

    in simple terms try drawing the volume element formed by the infintesimals, (approximating a infintesiaml cube in the limit..)
    [tex]
    dV = d\textbf{r} = r^2\sin{\theta}.dr.d\theta.d\phi
    [/tex]

    and you will see where the [tex]
    r^2{\sin{\theta}
    [/tex] terms comes from
     
  4. Mar 11, 2009 #3
    I'l presume also aside from using the Jacobian for the coordinate transom one should start with:

    [tex]\delta(x-x_o,y-y_o,z-z_o)=\delta(x-x_o)\delta(y-y_o)\delta(z-z_o)[/tex]
     
  5. Mar 11, 2009 #4

    lanedance

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    Homework Helper

    Cheers John, I've re-read the question - missed the meaning of delta first time round...

    element1945 can you elaborate on the problem at all? also do you understand what the 1 dimensional delta function is?
     
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