Recent content by Pierre13

  1. Pierre13

    Graduate Poisson's equation with Green's function for point charge

    PROBLEM FINALLY SOLVED! Thanks Orodruin! Your advice was very valuable! The "subtlety" that was puzzling me the whole time was actually a mistake I made. I just found what we were discussing about in my favourite textbook on Electrodynamics. There it says to get the potential due to a point...
  2. Pierre13

    Graduate Poisson's equation with Green's function for point charge

    First let me thank you a lot for taking your time and posting such an extensive and valuable answer! You are right, using the standard Green's function for a pure delta source without factors in front is desirable, so that one does not have to adapt it for different inhomogeneities. I found a...
  3. Pierre13

    Graduate Poisson's equation with Green's function for point charge

    sorry I meant ##D_\mathrm{op} = \nabla^2 - k^2##, the plus is for the case of the original (not the modified) Helmholtz equation.
  4. Pierre13

    Graduate Poisson's equation with Green's function for point charge

    Thanks for the reply! I agree with you that this should be a trivial problem. But as far as I see the convolution cannot be performed (being singular) and is also not giving the desired result ##\varPhi(\boldsymbol r) = \frac{q}{|\boldsymbol r - \boldsymbol r'|}##. At least I do not see how to...
  5. Pierre13

    Graduate Poisson's equation with Green's function for point charge

    Hello! I'm having a problem with the Green's function solution of the simplest case of Poisson's equation, namely a single test charge ##q## located at ##\boldsymbol r = \boldsymbol r'##. I've read the related posts on Poisson's equation via Green's function formalism, but they do not answer my...