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3d Fourier transform of function which has only radial dependence ##f(r)##. Many authors in that case define

[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##?

[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##?

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