Hey folks, I'm trying to find the Green function for the equation [tex]-\partial_\mu \partial^\mu \phi = K[/tex] where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that [tex]G|_0= G|_a=0[/tex] I've pretty much solved this problem for the case of NO boundary conditions, eg an infinte wave, I'm just stuck on where to put in info on the BC's. I am confident I have derived the following expression correctly as it matches with a book I am using: [tex](-\partial_z^2-\lambda^2)g(z,z')=\delta(z-z')[/tex] where [tex]\lambda^2=\omega^2-k^2 [/tex] So really this is the problem I need to solve - where g is the reduced Greens function. I can solve this by taking the FT and using contour integrals...pretty standard, but this is for an infinite wave. My question is 'where and how do I impose boundary conditions for g(0,z')=g(a,z')=0 ??'.