How can I correctly perform Fourier inversion of function S(q) to get G(r)?

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Discussion Overview

The discussion centers around the process of performing a Fourier inversion of a function S(q) to obtain G(r), specifically referencing equation 7.46. Participants are exploring the challenges and methods related to this mathematical transformation within the context of physics.

Discussion Character

  • Homework-related, Exploratory, Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to perform the Fourier inversion of S(q) to get G(r) from equation 7.46.
  • Another participant questions whether the request is for homework help.
  • A participant clarifies that they are learning physics and need to calculate this for their studies, indicating it is not homework.
  • There is a suggestion to use Wolfram Alpha for assistance with the Fourier inversion.
  • A participant mentions using Wolfram Alpha and obtaining a result similar to their own calculations, but notes a discrepancy with their textbook, which has a different variable in the denominator.
  • This same participant expresses concern about the correctness of their and Wolfram Alpha's results compared to the fundamental result in their book.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct method or results of the Fourier inversion. There are competing views regarding the accuracy of the results obtained through Wolfram Alpha and personal calculations compared to the textbook.

Contextual Notes

There are unresolved issues regarding the specific details of equation 7.46 and the implications of the variable differences noted by participants. The discussion reflects uncertainty about the correctness of the inversion results.

Who May Find This Useful

Individuals interested in Fourier transforms, particularly in the context of physics applications, as well as those learning about mathematical techniques in physics may find this discussion relevant.

enrikofermi
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Hi all.
I have to do Fourer inversion of an equation 7.46 but I don't know how to do that.
If anybody has any idea it wolud be very helpfull.
Inversion of S(q) is G(r).
 

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No. I'm learning some physics and need to calculate this to get next step, but i can't. :/
 
Did you try Wolfram Alpha?

I can't see the whole problem, plus it is sideways.
 
No, didn't. That is whole problem, to do Fourier inverse of 7.46. Sorry because it is sideways. :/
 
I have used Wolfram Alpha and got (almost) same result as I calculated earlier. (See pic) But in my book I have r instead of k in denominator. And that result in the book is fundamental! It must be correct. Where have Wolfram and me failed?
 

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