Student handout: Visualization of Quantum Probabilities for a Particle Confined to a Ring

Central Forces Spring 2021
Students see probability density for eigenstates and linear combinations of eigenstates for a particle on a ring. The three visual representations: standard position vs probability density plot, a ring with colormapping, and cylindrical plot with height and colormapping, are also animated to visualize time-evolution.
What students learn
  • Students use Mathematica to visualize eigenfunctions and linear combinations of eigenfunctions in one dimension on a ring.
  • Students use Mathematica to observe the time evolution of linear combinations of eigenfunctions
  • Students can review the relationship between visual and algebraic representations of wavefunctions in a simple context before working with the more complicated functions in the hydrogen atom solution.

Use this Mathematica notebook or this GeoGebra applet to explore the time dependence of quantum states on a ring.

Author Information
Corinne Manogue, Kerry Browne, David McIntyre
central forces quantum mechanics angular momentum probability density eigenstates time evolution superposition mathematica
Learning Outcomes