I agree with your assessment of the way Jackson uses the identities, I just wanted to exercise myself and try to see if there really was an easy approach to integrate by parts in the conventional sense. I completed two semesters studying EM from Jackson's book, but it was over fifteen years ago...
I understand that the integration by parts that I posted is a very naive attempt at following the statement by Jackson that the result can be obtained by an integration by parts. Using your suggestion of ##\Phi \nabla^2 \Phi = \nabla \cdot (\Phi \nabla \Phi) - |\nabla \Phi|^2## is very...
I am reviewing Jackson's "Classical Electromagnetism" and it seems that I need to review vector calculus too. In section 1.11 the equation ##W=-\frac{\epsilon_0}{2}\int \Phi\mathbf \nabla^2\Phi d^3x## through an integration by parts leads to equation 1.54 ##W=\frac{\epsilon_0}{2}\int |\mathbf...
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I am Brazilian, have a MD in Computational Physics and will soon resume my PhD in Statistical Mechanics. I want to have a solid career in theoretical physics centered on Statistical Physics and Non...