Two dimensional green function

[welshtill]

In studying the scattering problem, one should know green function in free space. while in two dimension, green function is the hankel function, seen in the attached file. bu i got confused in the second equation in the attached file. could anyone give me some details about this relationship? it will be of great help for me, thanks forwardly!

i know this is not suited for me to post it here, but i think it is a very important relationship if one want to study two dimensional scattering problem. i have post it in the homework section, but without any answer.

 

[shawl]

It's hard for me to understand what you are confused.

I am not familiar with these equation, but I give you a website for the Bessel function and Hankel function.

You may make your confusion clear. And it will be better if you show the book's name as possible.

 

[welshtill]

thanks for shawl, i am sorry that i forgot to post the book's name.the attached file is taken from "methods of theoretical physics, part 2" by Philip M. Morse and Herman Feshbach, on page 1362.

 

[welshtill]

what confused me is this equation:

i cann't find anywhere the derivation of this relation.