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I am trying to find the inverse Fourier transform of: $$ F(k_x,k_y)=e^{ikz} e^{-ik_\rho ^2 z /2k}, $$ where $k^2 = k_x^2 +k_y^2 +k_z^2 = k_\rho ^2 +k_z^2 $ is a constant.

I am getting confused as to how to go about this. Inverse fourier transform of $F(k_x)$ would be given by $ \int F(k_x)e^{-ik_x x} \frac{dk_x}{2\pi} $? How do I change this when there is a function of two variables?

Furthermore, could anyone explain what is meant by the prefactor of the exponential?

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  • $\begingroup$ This thesis chapter has a nice discussion on higher dimensional Fourier transforms. $\endgroup$ – Chris Mueller Feb 13 '14 at 20:59
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    $\begingroup$ Is the $z$ in the exponential just a constant? $\endgroup$ – JeffDror Feb 13 '14 at 22:02
  • $\begingroup$ I guess so but i'm not sure... the question doesn't state $\endgroup$ – user1887919 Feb 14 '14 at 9:30

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