Sep 25, 2025
A trilogy in five+ parts: Confirming an error in the derived 1D Helmholtz Green's function.
[Click here for a PDF version of this, and previous, posts in this series]. The discontinuity in the derived 1D Helmholtz Green’s function is somewhat surprising. Let’s try to verify that this works or find what does. The first think to check is that \begin{equation}\label{eqn:helmholtzGreens:1220} \lr{ \spacegrad^2 + k^2} G(x,x’) = 0, \end{equation} at locations where \( x \ne x’ \). Since we…
