An electron approaching an stationary atomic target with a given velocity can elastically scatter off the target. We will calculate the differential cross section for the elastic scattering of electrons from atomic hydrogen in the Born approximation.
is the differential scattering cross section in the Born approximation. For a spherically symmetric potential V(r)=V(r), this yields
Here 
We use
We integrate using Simpson’s rule. The figure below compares the cross sections as a function of scattering angle obtained using the Born approximation and the partial wave method.
