Visualizing Eigenfunctions

We have a number of Mathematica/Maple-based activities that allow students to visualize quantum mechanical eigenfunctions. For particle in a box or the particle confined to a ring, since the functions are quite simple, the visualizations explore the time dependence of the wave functions and their probabilities. For more complicated wave functions, such as the rigid rotor or the hydrogen atom, we currently have activities which explore the probability density only. We hope to have time-dependent activities soon.


  • Particle Confined to a Ring: This computer visualization activity represents the probability density of a particle confined to a ring. Students are able to visualize linear combinations of eigenstates and animate time evolution of the probability density. The probability density is shown using three distinct, but equivalent, representations which demonstrates to students how to move between representations which is an important skill for professional physicists and other disciplines.
  • Linear Combinations of Spherical Harmonics: Students use Mathematica (or Maple) to visualize various representations of probability densities of linear combinations of spherical harmonics. Students can explore various linear combinations by mapping them onto a sphere and a polar plot. This follows from the Visualization of the Spherical Harmonics activity where spherical harmonics were represented similarly; students find that all of the spherical harmonics have spherical symmetry. In this activity, students discover that linear combinations of spherical harmonics are not necessarily spherically symmetric.

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