Use your result in Problem 10.16 to develop the Born approximation for one-dimensional scattering (on the interval - < x < , with no brick

Use your result in Problem 10.16 to develop the Born approximation for one-dimensional scattering (on the interval -∞ 0(x) = Ae^ikr, and assume Ψ(x0) ≈ Ψ₀(x0) to evaluate the integral. Show that the reflection coefficient takes the form:

Problem 10.16

Find the Green’s function for the one-dimensional Schrödinger equation, and use it to construct the integral form (analogous to Equation 10.66).

m R ~ (FK) x kx V (x) dx . e21kx hk -x (10.103)