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Mandl and Shaw, page 16, eqn (1.56)

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

2. Homework Equations
[tex]{E}_L = -\nabla\phi[/tex]
[tex]{\nabla}^2\phi = -\rho[/tex]


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

By the way, I have the 1993 revised edition.
 
Last edited:
Thanks malawi_glenn, that's what I needed.
 

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