Express electrostatic potential as a Fourier integral

[zheng89120]

Homework Statement

The charge distribution of an atomic nucleus is modeled by the Gaussian distribution:

p(r) = A exp(-r²/a²)

Obtain the Fourier transform of p(r), and use the result to obtin an expression for the potential as a Fourier integral.

Homework Equations

Fourier transform and electrostatics

The Attempt at a Solution

I found the Fourier transform to be A*pi^3/2*a³ exp(-1/4*a²k²)

How would you obtain the electrostatic potential (I suppose V) as a Fourier integral?

 

[vela]

Express $\rho(r)$ as a Fourier integral and then substitute that into the integral for calculating the potential.