The Lippmann-Schwinger equation for the scattering state ∣ψ⟩ is:
∣ψ⟩=∣ϕ⟩+E−H0+iϵ1V∣ψ⟩
where ∣ϕ⟩ is a free-particle state with energy E.
(a) Show that this equation is equivalent to the Schrödinger equation (H0+V)∣ψ⟩=E∣ψ⟩ with the appropriate boundary conditions.
(b) Iterate once to derive the Born approximation.