Green's function expansion in a set of eigenfunctionby kristobal hunta Tags: eigenfunction, expansion, function, green 

#1
Sep2204, 09:18 PM

P: 7

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
Sep2304, 09:32 PM

Sci Advisor
PF Gold
P: 1,458

Look in Jackson's Electrodynamics book, I believe that the solution can be found by applying either chapter 2 or 3's methods.




#3
Oct404, 02:36 AM

P: 1

i want notes about quantum dynamics(schrodinger,heisenberg and interaction representation or pictures of quantum mechanics)



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