Two dimensional green function

In summary, the conversation is about the green function in free space and its relationship to the hankel function in two dimensions. The person is confused about the second equation in the attached file and is asking for more details and clarification. They have also posted this question in the homework section without receiving an answer. They are looking for help understanding this equation and have provided the book title and page number where it is found.
  • #1
welshtill
13
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
what confused me is this equation:
QQ截图未命名.jpg

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

1. What is a two dimensional green function?

A two dimensional green function is a mathematical tool used in quantum mechanics to describe the behavior of a particle in a two-dimensional space. It is a solution to the Schrödinger equation that takes into account the boundary conditions of the system.

2. How is a two dimensional green function different from a one dimensional green function?

A two dimensional green function takes into account the additional dimension of space, whereas a one dimensional green function only considers one dimension. This allows for a more accurate description of the behavior of a particle in a two-dimensional space.

3. What is the importance of using a two dimensional green function?

Using a two dimensional green function allows for a more accurate and realistic description of the behavior of a particle in two-dimensional systems, which are commonly found in nature. It is also a useful tool in solving many problems in condensed matter physics and quantum mechanics.

4. How is a two dimensional green function calculated?

A two dimensional green function is usually calculated using integral equations or numerical methods, such as the finite difference method or the Monte Carlo method. These methods involve solving the Schrödinger equation with appropriate boundary conditions to obtain the green function.

5. What are the applications of a two dimensional green function?

A two dimensional green function has many applications in quantum mechanics, such as in the study of electronic and magnetic properties of materials, quantum transport phenomena, and the behavior of quantum dots and wires. It is also used in other fields, such as electromagnetism and acoustics, to study wave propagation in two-dimensional systems.

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