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Time Evolution of a Gaussian Wave Packet: Instructor's Guide

Main Ideas

  1. Gaussian wave packet
  2. Dispersive waves

Students' Task

Estimated Time: 15 minutes

Students are challenged to think about the time evolution of a Gaussian distribution.

Prerequisite Knowledge

  • Non-dispersive waves
  • Wave properties
  • Fourier Transforms
  • Traveling and Standing waves


Activity: Introduction

This activity can be used to help the students visualize how dispersive waves propagate in space. Prior to this activity, students were given lecture about time dependence of the Schrodinger's equation. An animation of Gaussian distribution then presented to the class.

Activity: Student Conversations

  • Students typically run into trouble attempting to apply classical intuition to the task; students have internalized the motion of a rope, guessing that the packet might reduce in amplitude and propagate to the right as time increases. Some students guess that the packet will disperse, but this is rare.
  • This activity is great for review, since the content is deeply rooted in material previously covered in the course.

Activity: Wrap-up

Emphasis on the solution of Schrodinger's equation is a dispersive wave equation.


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