Two dimensional green function

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Discussion Overview

The discussion revolves around the two-dimensional Green function in the context of scattering problems. Participants are exploring the relationship involving the Hankel function and seeking clarification on a specific equation from a referenced text.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant notes the importance of the Green function in free space for studying two-dimensional scattering problems and expresses confusion regarding a specific equation related to the Hankel function.
  • Another participant offers a suggestion to clarify the confusion by providing a reference to resources on Bessel and Hankel functions, indicating a lack of familiarity with the equations in question.
  • A participant later identifies the source of the attached file as "Methods of Theoretical Physics, Part 2" by Philip M. Morse and Herman Feshbach, which may provide context for the discussion.
  • There is a specific request for the derivation of a particular relationship, indicating a gap in understanding that the participant is seeking to fill.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing confusion and seeking clarification without reaching a consensus on the specific equation or its derivation.

Contextual Notes

Limitations include the lack of clarity on the specific equation in question and the absence of derivation details that may be necessary for understanding the relationship involving the Hankel function.

welshtill
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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.
 

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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.
 
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.
 
what confused me is this equation:
QQ截图未命名.jpg

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

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