3D fourier transfrom

  • Thread starter Marthius
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  • #1
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I need to take the 3-Dimensional Fourier transform of a point charge potential. I have an integral of this form, but I am unsure as to how to approach this integral.

[tex]\int e^{-i\vec{x}\vec{k}} \frac{q}{|\vec{x}-\vec{x'}|}d^3x[/tex]

A push in the right direction would be appreciated.
 

Answers and Replies

  • #2
Meir Achuz
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Introduce the variable [tex]{\vec r}={\vec x}-{\vec x}'[/tex].
 
  • #3
mathman
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Change from Cartesian to spherical coordinates.
 
  • #4
Meir Achuz
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It was not in Cartesian coordinates.
 
  • #5
mathman
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It was not in Cartesian coordinates.

What do you mean by d3x?
 
  • #6
Meir Achuz
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d^3x usually just means the volume differential, not necessarily in cartesian coords.
 
  • #7
mathman
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In order to carry out the integration, the volume differential should be expressed explicitly in some coordinate system. I recommend using spherical.
 

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