- The effect of angular momentum, the force constant, and the reduced mass on the shape of the effective potential function;
- Practicing exploring parameter space for a function;
- Developing intuition about how the orbit shape depends on these parameters.
- How to represent 3-d scalar fields in several different ways;
- The symmetries of a some simple charge distributions such as a dipole and a quadrupole.
Students use prepared Sage code to predict the gradient from contour graphs of 2D scalar fields.
Mathematica Activity
30 min.
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.
Students use Mathematica to visualize the probability density distribution for the hydrogen atom orbitals with the option to vary the values of \(n\), \(\ell\), and \(m\).
Students observe three different plots of linear combinations of spherical combinations with probability density represented by color on the sphere, distance from the origin (polar plot), and distance from the surface of the sphere.