Use your result in Problem 10.16 to develop the Born approximation for one-dimensional scattering (on the interval -∞ < x < ∞, with no “brick wall” at the origin). That is, choose Ψ₀(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).

Transcribed Image Text:

m R≈ ~ (FK) ² x ²¹kx V (x) dx ³². e21kx h²k -∞x (10.103)