# Mandl and Shaw, page 16, eqn (1.56)

1. Feb 28, 2009

### Jimmy Snyder

1. The problem statement, all variables and given/known data
$$\int{E}_L^2d^3x = \int\frac{\rho(x)\rho(x')}{4\pi|x - x'|}d^3xd^3x'$$

2. Relevant equations
$${E}_L = -\nabla\phi$$
$${\nabla}^2\phi = -\rho$$

3. The attempt at a solution
$$\int{E}_L^2d^3x = \int(\nabla\phi)^2d^3x = -\int\phi\nabla^2\phi d^3x = \int\rho(x)\phi(x)d^3x$$
I suppose to finish up, I need to see why
$$\phi(x) = \int\frac{\rho(x')d^3x'}{4\pi|x - x'|}$$
But I don't see it. Or am I on the wrong track.

By the way, I have the 1993 revised edition.

Last edited: Feb 28, 2009
2. Feb 28, 2009

### malawi_glenn

Last edited: Feb 28, 2009
3. Feb 28, 2009

### Jimmy Snyder

Thanks malawi_glenn, that's what I needed.