[Click here for a PDF version of this post] Here is a summary of Green’s functions for a number of gradient related differential operators (many of which are of interest for electrodynamics, and most of them have been derived recently in blog posts.) These Green’s functions all satisfy \begin{equation}\label{eqn:deltaFunctions:120} \delta(\Bx – \Bx’) = L G(\Bx, \Bx’). \end{equation} Let \( \Br =…

[Click here for a PDF version of this post, and the previous posts in this series.] We used a complicated limiting argument to show that the \( \mathrm{sgn}(x – x’) \) factor in the contour integral derivation of the Helmholtz operator Green’s function was wrong. Having discovered, even if slightly by accident, what the correct form of that Green’s function is, we can check it more directly. This…

[Click here for a PDF version of this post] This is a continuation of yesterday’s post on wave function Green’s functions. We derived the 1D Green’s function, now it’s time for the 3D. Next up after this will be the 2D Green’s function, which looks harder to evaluate than the 1D or 3D versions. 3D Green’s function. The 3D Green’s function that we wish to try to evaluate…