Central Forces 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.
- Editor
- maggie
- Author Information
- Corinne Manogue, Kerry Browne, David McIntyre
- Keywords
- central forces quantum mechanics angular momentum probability density eigenstates time evolution superposition mathematica
- Prerequisite
Knowledge
-
- Students should have some familiarity with Maple. In particular, they need to know how to navigate a worksheet, execute exiting commands, edit commands, and manipulate animation plots.
- Students should be familiar with the eigenfunctions and time evolution for the motion of a particle confined to a 1-D ring.
- Learning Outcomes
-
- Publication Status
- Published
- Publication Date
- July 11, 2023, 11:45 p.m.