- #1

Angelo Cirino

- 3

- 3

u = \Phi, dv = \mathbf \nabla^2\Phi d^3x=\mathbf \nabla \cdot (\mathbf \nabla \Phi) d^3x, du=\mathbf \nabla \Phi d^3x, v = \mathbf \nabla \Phi\\

\int \Phi \mathbf \nabla^2\Phi d^3x=\Phi \mathbf \nabla \Phi - \int \mathbf \nabla \Phi \cdot \mathbf \nabla \Phi d^3x=\Phi \mathbf \nabla \Phi - \int \mathbf |\mathbf \nabla \Phi|^2 d^3x

$$ that is obviously wrong, the term ##\Phi \mathbf \nabla \Phi=-\Phi \mathbf E## shouldn't be there and it is a vector quantity summed to a scalar. How I should proceed?