Fourier transform of wave-function in 4D space

[spex]

hi, there

hope someone can help me

the task is simple, i have to calculate the Fourier tranform of wave-function to get it in momentum space

the problem is that this is a 4-dimensional space, so the Fourier transform is multi-dimensional

the only idea i have is that this wave-function has a hyperspherical harmonic as its part, so i guees the book of Avery J. 'Hyperspherical Harmonics: Application to Quantum Theory' can help

but i can't get it( has anyone seen it? an electronic version, i can't afford to get a printed version(

also I've read that maybe Fock method can help, but this method is also desribed in the same book(

cheers, Max

 

[turin]

Did you try using a kernel of the form:

e^(i(p^μx_μ)/h) = e^i(ωt-k.x)?

Is there some reason why you would think this is inappropriate?

 

[spex]

thank you for your feedback

i do use this kernel to calculate Fourier transform, but the problem is that Schrödinger equation is solved not in ordinal coordinate space but in new 'hyperspherical' coordinates - rho, psi, theta, phi

so when i start to calculate Fourier transform i have to replace x, y, z, t with their expressions in hyperspherical coordinates so the task becomes more complicated

and i hope that Avery's book gives the way how to calculate it

 

[turin]

Sorry spex.
I thought you were just asking about the generalization from 1-D to n-D Fourier transform.

I don't know how to do what you are trying to do, and I know nothing of "Avery's book."

 

[spex]

ah... damn

do you know anything on Hankel or Watson transform? or any place where i can find more info about them?

 

[turin]

I've never heard of the Watson transform, but I found a brief table of Hankels on the internet. I think it was on that Mathworld website. I'll see if it can find it again and then post the link.

http://mathworld.wolfram.com/HankelTransform.html