For the hydrogen atom in its ground state, the electron density is $n(r) = (\pi a_0^3)^{-1}\exp(-2r/a_0)$, where $a_0$ is the Bohr radius. Integrating this expression over all space yields 1 indicating that there is one electron.

\begin{equation} \int \limits_0^{\infty} 4\pi r^2 n(r)dr=1 \end{equation}

Show that the Fourier transform of this function in the [1,-1] notation is $F(k) = 16/(4 + k^2a_0^2)^2$.