Electron-electron potential energy

Write a main program which uses your subroutines to compute the ``Hartree'' electron-electron potential energy for the 1s state,

$$V_{\mathrm el-el} = \frac{1}{2} \int \phi(\vec x) n(\vec x) ... ... \int_0^\infty \phi_{1s}(r) \psi_{1s}^2(r) \, 4 \pi r^2 \, dr.$$

Note: For $n(\vec x)=\psi_{1s}^2(\vec x)$, the potential from Poisson's equation $\nabla^2 \phi_{1s}(\vec x) = - 4 \pi n_{1s}(\vec x)$ is

$$\phi_{1s}(r)=\frac{1-e^{-2r}}{r}-e^{-2r}.$$

Hint: endpoints ...