This is the maths part of a physics problem - that of the solution of Schrodinger equation for a 3D harmonic oscillator in spherical coordinates. The solution is a product of associated Laguerre functions multiplied with Gaussians (this much for the radial part), multiplied with the spherical harmonics, since the Hamiltonian has spherical symmetry. The problem is, I am supposed to normalize them in momentum space, using the condition:
$N^2 \int d^3k \ \psi^* \psi = (2\pi)^3$. where \psi is the momentum space wavefunction, in 3D, and N is the norm. Now, the radial part of the integral is not very hard to evaluate, but I have no experience with solution of the angular part. I mean, first, how do I get the FT of spherical harmonics, and second, solve this integral to arrive at the norm?
Maybe, my troubles originate from the fact that while I have some experience with FT's of the kind encountered in e.g. the radial part, I have never encountered the FT of spherical harmonics before. So, I would be extremely grateful if someone recommends me a basic text in case my question appears trivial.
PS - I know some of the suggestions would be to solve this equation right away in momentum space. But I have been asked to do it in this brute force manner first, before I start looking at alternatives.
Thanks.