URGENT - Green's Function Solution to Poisson/Helmholtz equations

popffabrik

hey, i have an exam pretty soon and couldnt find any answers/hints on how to do this:

1.How do you express the solution f(x') of the Helmholtz equation in terms of the green function g(x,x') in integral form, with dirichlet or neumann conditions?

2.What is the condition on the Green's function on the surface S for a poisson equation with neumann bc on S? and how do you get the integral solution up to an undetermined constant?

would be great if someone can help, ml

HallsofIvy

There are whole books written on these topics! We might be able to answer specific questions but I don't think anyone can give you a whole tutorial on this.

popffabrik

hey, i just need a specific integral solution for the helmholtz equation using greens function, assuming that it acts in 3d and is spherically symmetric (only dependent on the distance of the centre of the dirac function)