The Born approximation yields f(k,k′)≃m2πℏ2∫ei(k−k′)⋅r′V(r′)d3r′. Thus, \(f({\bf k},{\bf...The Born approximation yields f(k,k′)≃m2πℏ2∫ei(k−k′)⋅r′V(r′)d3r′. Thus, f(k,k′) becomes proportional to the Fourier transform of the scattering potential V(r) with respect to the wavevector q=k−k′.
We just need the result that we obtained for a constant perturbation, Fermi’s Golden Rule, to compute the rate of transitions between the initial state (free particle of momentum p) to the f...We just need the result that we obtained for a constant perturbation, Fermi’s Golden Rule, to compute the rate of transitions between the initial state (free particle of momentum p) to the final state (free particle of momentum p′). Vk′k≡⟨k′|ˆV|k⟩=∫∫∫u∗k′(r)V(r)uk(r)dτ.
