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 timeevolution.
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
 Keywords
 central forces quantum mechanics angular momentum probability density eigenstates time evolution superposition mathematica
 Learning Outcomes
