1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Green's function expansion in a set of eigenfunction

  1. Sep 22, 2004 #1
    Hi! I encountered the problem that I need to decompose the Green function into a set of eigenfunction. Particularly, I have the free space Green function
    [tex] G(\vec r; \vec r') = \frac {e^{i k | \vec r - \vec r'|} } {4 \pi | \vec r - \vec r'|} [/tex]
    and I need to express it into series of cylindrical mode eigenfunctions
    [tex] \Psi ( \vec r; k) = H_m ( q r) sin( h z) e^{i m \phi} [/tex]
    [tex] k^2 = q^2 + h^2, h = \frac { \pi } {2 L} [/tex]

    here H - Hankel's function of the first kind.
    Eigenfunction forms a complete set, with discrete spectrum of eigenvalues q and h.
    I know that we can decompose the Green function into set of eigenfunctions, but I have the Green function for spherical representation, and eigenfunctions are from waveguide formed by two infinite plates parallel to each other. I couldn't find anything relevant about expanding the Green function into arbitrary set of eigenfunctions. Would appreciate any opinion or advice on the matter :)
  2. jcsd
  3. Sep 23, 2004 #2

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    Look in Jackson's Electrodynamics book, I believe that the solution can be found by applying either chapter 2 or 3's methods.
  4. Oct 4, 2004 #3
    i want notes about quantum dynamics(schrodinger,heisenberg and interaction representation or pictures of quantum mechanics)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Green's function expansion in a set of eigenfunction
  1. Green's function (Replies: 6)

  2. Green functions (Replies: 3)