Curl of a Div of a Green's Function

1. Mar 10, 2007

pqnelson

Okey Dokey, so I'm bored and decided to play around with some math. I've got a problem that I can't figure out now; I have the green's function for the laplacian

$$G(\vec{x}, \vec{x'}) = - \frac{1}{4\pi |\vec{x} - \vec{x'}|}$$

There are no boundary conditions.

Is there any lazy way to figure out the div of the curl of the green's function, or do I have to do some work on this one?

[EDIT]: The lack of coffee is getting to me, it's the curl of a gradient of the green's function.

2. Mar 11, 2007

lalbatros

div(curl(A))=0 for any vector A

3. Mar 11, 2007

HallsofIvy

Staff Emeritus
The OP editted it to curl(grad f) but it easy to show that that is 0 also!

$$\left|\begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ f_x & f_y & f_z \end{array} \right|= \vec{0}$$

It doesn't matter whether the function is Green's function or not.