Show that the Dirac function defined as $$\delta)(\rho-\rho_0)=\frac{1}{4\pi} \bigtriangleup \frac{1}{|\rho-\rho_0|} $$
where $\rho=(x_1,x_2,x_3),\rho_0=(x_{1,0},x_{2,0},x_{3,0})$ and $\bigtriangleup=\bigtriangledown \cdot \bigtriangledown = div \ grad$ fullfills
- $\delta(\rho-\rho_0)=0 \ \forall \rho \ne \rho_0$
- $\int_Vd^3r\delta(\rho-\rho_0)=1$ if $\rho_0 \in V$ and $0$ otherwise.
This is someone's solution.
I mean what is this,,,shouldnt you use multiple integration to solve this? And if so, how does that go? Everytime when it comes to dirac i just lose it...