3d Fourier transform of function which has only radial dependence ##f(r)##. Many authors in that case define(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec{k} \cdot \vec{r}=|\vec{k}||\vec{r}|\cos\theta[/tex]

where ##\theta## is angle in spherical polar coordinates.

So

[tex]\frac{1}{(2\pi)^3}\int\int_{V}\int e^{-i \vec{k} \cdot \vec{r}}f(r)=\frac{1}{(2\pi)^3}\int^{\infty}_0r^2f(r)dr\int^{\pi}_0\sin \theta d\theta \int^{2 \pi}_0 d\varphi e^{-ikr\cos \theta}[/tex]

Ok function ##f(r)## does not depend on angles, but why here we have specially angle ## \theta##?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fourier transform of function which has only radial dependence

**Physics Forums | Science Articles, Homework Help, Discussion**