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.

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 \(m\).

Spherical harmonics are continuous functions on the surface of a sphere.

The \(\ell\) and \(m\) values tell us how the function oscillates across the surface.

Spherical harmonics are complex valued functions.