Chapter 7: The Schrödinger Equation

Introduction

In the previous chapter we began our discussion of quantum mechanics with the wave function and Born's probabilistic interpretation. We now consider the process of how to determine wave functions, the energy of these states, and also how to determine how they evolve in time. To do so, we need look no further than the Schrödinger equation.

Sections

Section 7.1: Classical Energy Diagrams.
Section 7.2: Wave Function Shape for Piecewise-constant Potentials.
Section 7.3: Wave Function Shape for Spatially-varying Potentials.
Section 7.4: Exploring Energy Eigenstates Using the Shooting Method.
Section 7.5: Exploring Energy Eigenstates and Potential Energy.
Section 7.6: Time Evolution.
Section 7.7: Exploring Complex Functions.
Section 7.8: Exploring Eigenvalue Equations.

Problems

Problem 7.1: Match the wave function with the correct potential energy function.
Problem 7.2: Determine the wave function for a ramped potential energy well.
Problem 7.3: A time dependent wave function for a plane wave is shown.
Problem 7.4: Determine the complex wave function given in the top graph.