Use the one-dimensional Born approximation (Problem 10.17) to compute the transmission coefficient (T = 1-R) for scattering from a delta function (Equation 2.117) and from a finite square well (Equation 2.148). Compare your results with the exact answers (Equations 2.144 and 2.172).

Problem 10.17

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:

Transcribed Image Text:

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