Chapter 9: Scattering in One Dimension

Introduction

We now consider another one-dimensional problem, the scattering problem. In doing so we need to consider scattering-type solutions and what they mean. For standard scattering situations, the wave functions we use are usually those valid for regions of constant potential energy such as complex exponentials (plane waves) when E > V₀ and real exponentials when E < V₀.¹

Sections

Section 9.1: The Scattering of Classical Electromagnetic Waves.
Section 9.2: Exploring Classical and Quantum Scattering.
Section 9.3: The Probability Current Density.
Section 9.4: Plane Wave Scattering: Potential Energy Steps.
Section 9.5: Exploring the Addition of Two Plane Waves.
Section 9.6: Plane Wave Scattering: Finite Barriers and Wells.
Section 9.7: Exploring Scattering and Barrier Height.
Section 9.8: Exploring Scattering and Barrier Width.
Section 9.9: Exploring Wave Packet Scattering.

Problems

Problem 9.1: What happens to the classical wave during scattering?
Problem 9.2: Describe each of the potential energy functions that the incident plane wave is experiencing.
Problem 9.3: Describe each of the potential energy functions that the incident plane wave is experiencing.
Problem 9.4: Rank the regions by kinetic energy, potential energy, and the energy of the incident plane wave.
Problem 9.5: Determine the constant potential energy in each region.
Problem 9.6: Describe each of the potential energy functions that the incident plane wave is experiencing.

__________ ¹There is one other possibility that is not often considered. If E = V₀, the solution to the Schrödinger equation yields a linear solution.