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Time Evolution of a Gaussian Wave Packet

Keywords: Oscillations & Waves, Wave Packets, Gaussian, Time Evolution, Middle Division

Highlights of the activity

  1. This computer visualization activity is designed to help upper-division undergraduate students understand the time evolution of a Gaussian wave packet.
  2. Students predicted the time evolution of a Gaussian distribution.
  3. The whole class discussion emphasizes that the solution to time-dependent Schrodinger's equation is a dispersive wave and focuses the difference between the dispersion relation for classical and quantum waves.

Reasons to spend class time on the activity

The free particle is one of the most fundamental quantum situations considered in advanced quantum courses and also one of the most complex of the archetypal examples. We discuss the Gaussian probability distribution with regards to transforming between position space and momentum space, and the connection between these representations of the wave function and the Heisenberg Uncertainty Principle. We emphasize the contrast between the non-dispersive wave equations considered in the classical context with the dispersive nature of solutions to the Schrödinger Equation.

This activity works particularly well when sequenced with other activities:

Examples of Quantum Systems

Time Evolution

Uncertainty Principle


Instructor's Guide

Mathematica Notebook


Authors: Janet Tate, Elizabeth Gire
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