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

#### Jimmy Snyder

1. Homework Statement
$$\int{E}_L^2d^3x = \int\frac{\rho(x)\rho(x')}{4\pi|x - x'|}d^3xd^3x'$$

2. Homework 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.

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#### Jimmy Snyder

Thanks malawi_glenn, that's what I needed.

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