1. The problem statement, all variables and given/known data Find the Green's Function for the Helmholtz Eqn in the cube 0≤x,y,z≤L by solving the equation: [itex]\nabla[/itex] 2 u+k 2 u=δ(x-x') with u=0 on the surface of the cube This is problem 9-4 in Mathews and Walker Mathematical Methods of Physics 2. Relevant equations Sines, they have the properties we're looking for. 3. The attempt at a solution So, if the solution is in one dimension we obviously have G=asinkx x<x' and G=bsink(x-L) for x>x' And these are obtained by solving [itex]\nabla2[/itex]u+k2u=0 and looking for a and b based on the matching condition at x'. I'm wondering if I can do the same thing for this three dimensional case, using separation of variables and solving for k^2 as the eigenvalue. Then enforcing orthogonality on the functions I get. My problem with this is just that it seems very awkward to have eight sets of equation for the Green's function, based on whether x<x' while y>y' and z<z' for example. Any help appreciated.