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Diract delta function

1. Homework Statement
Justify the following expretion, in spherical coordinates;

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


2. Homework Equations



3. The Attempt at a Solution

I dont know what it means.... please help?
 

lanedance

Homework Helper
3,304
2
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
 
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]
 

lanedance

Homework Helper
3,304
2
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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