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how do I find the Fourier transform of a function that is separable into a radial and an angular part: $f(r, \theta, \phi)=R(r)A(\theta, \phi)$ ?

Thanks in advance for any answers!

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    So, unless you can easily express $A(\theta,\phi)$ in terms of the angle between $\vec{k}$ and $\vec{r}$, you'll probably not gain much.2011-04-21

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You can use the expansion of a plane wave in spherical waves. If you integrate the product of your function with such a plane wave, you get integrals over $R$ times spherical Bessel functions and $A$ times spherical harmonics; you'll need to be able to solve those in order to get the Fourier coefficients.

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    In cartesian coordinates it is "worth gold" to know that a function is separable; can be written as a product of a x dependent, y dependent and z dependent function: f(x,y,z)=X(x)Y(y)Z(z). E.g. rect(x, y, z) = rect(x)*rect(y)*rect(z) => F{ rect(x, y, z) } = sinc(x)*sinc(y)*sinc(z), where rect is the boxcar function. I am just a bit disappointed that the "separable property" (don't know what to call this properly) is not worth so much in spherical coordinates. The thing is that I map my problem to cartesian coordinates and use FFT, but I would like to utilize the "separable property" somehow.2011-04-21