Scattering: 1-D

Abstract

Most of what we know about the structure of matter comes from scattering experiments. When I discuss scattering in 3-D, I will review classical scattering theory, but for the time being, I want to discuss the scattering problem in one dimension. Scattering is simple in principle - send something in and see what comes out. I will give a detailed analysis of scattering in one dimension for the step potential shown in Fig. 17.1 and then give a qualitative discussion for other potentials. The step potential can be written as V (x) = V (x) = V0 Θ(x), where Θ(x) is the Heaviside step function which is zero for x < 0 and one for x ≥ 0.Fig. 17.1Step potential: (a) Energy less than the barrier height. (b) Energy greater than the barrier height