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(adsbygoogle = window.adsbygoogle || []).push({});

[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 :)

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# Green's function expansion in a set of eigenfunction

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