Show that the scattering amplitude in the Born approximation can be written as
f(θ)=−2πℏ2m∫ei(k′−k)⋅rV(r)d3r
where k is the incident wave vector and k′ is the scattered wave vector, with ∣k∣=∣k′∣=k. For a spherically symmetric potential, reduce this to a one-dimensional integral.