This applet generates three-dimensional pictures of spherical harmonics. The user can specify the quantum numbers L and M, the polar resolution, the azimuthal resolution, whether a mesh should be drawn, and whether to color the graphic by simulated lighting or by complex phase. The user can also enlarge or shrink the graphic and rotate it by dragging with the mouse.
Three-dimensional visualization of spherical harmonics.
Target Student Population:
Prerequisite Knowledge or Skills:
Introductory Quantum Mechanics
Type of Material:
Evaluation and Observation
Nifty graphics and efficient programming.
The applet does a reasonable job of displaying a 3D plot of some aspect of the spherical harmonics up to L = 5.
The plot can be shown in more or less detail, taking more or less time to plot, respectively.
What the plots represent is not clear; they do not represent spherical harmonics, which are complex.
That the two coloring schemes often produce completely different plots is puzzling. It appears that the "illuminated by light sources" option generates polar plots of absolute values of the real parts of spherical harmonics, whereas the "colored by complex phase" option generates polar plots of the absolute squares of the spherical harmonics.
No axis is shown.
The user must be sure to choose a tightly enough spaced grid to show the spherical harmonic correctly. Too small a number for the resolution gives a misleading plot.
Potential Effectiveness as a Teaching Tool
Recommended Use for Material: Lecture/Demo
Three-dimensional polar plots of the absolute squares of the spherical harmonics are helpful for visualizing the angular probability distribution of the hydrogen atom and the probability density of rotational states of a rigid rotator or a dumbbell molecule.
It is an attractive interface and plot, which makes the user more apt to play with it.
There is no indication as to what the plots represent. This lack of clarity significantly diminishes the usefulness of this applet.
The terms "illuminated by light sources" and "colored by complex phase" require explanation.
General Comments on Effectiveness: The material has an important place in a quantum course, but the usefulness of this applet is limited.
Ease of Use for Both Students and Faculty
The interface is very intuitive, easy to use.
No instructions are given to help on the choice of resolution.