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Particle Confined to a Ring

Keywords: Central Forces, Quantum Mechanics, Angular Momentum, Probability Density, Eigenstates, Multiple Representations, Maple, Mathematica, Computer Visualization

Highlights of the activity

  1. This computer visualization activity is designed to help students to visualize the probability density of a particle confined to a ring.
  2. Students use Maple or Mathematica to calculate the probability density from the particle's wavefunction, visualize linear combinations of eigenstates, and animate how the probability density changes with time.
  3. The entire class wrap-up discussion focuses on sharing three equivalent representations of the probability density and shows students how to move between the different representations.

Reasons to spend class time on the activity

The Maple worksheet provides three different (equivalent) representations of the probability density. Being able to use all three representations and understand their equivalence is a landmark on the students' path to becoming professional physicists. To address the important issues of stationary states and time-dependent states, students are later asked to animate these plots as a function of time for the case where the angular momentum eigenstates have different energies.


Instructor's Guide

Maple Worksheet (Maple 13)

cfqmring.mws (Maple 11 Classic)

Mathematica Notebook


Authors: Corinne Manogue, Kerry Browne, David McIntyre
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