Post a composite review
Unpost a composite review
Search all MERLOT
Select to go to your profile
Select to go to your workspace
Select to go to your Dashboard Report
Select to go to your Content Builder
Select to log out
Search Terms
Enter username
Enter password
Please give at least one keyword of at least three characters for the search to work with. The more keywords you give, the better the search will work for you.
Select OK to launch help window
Cancel help


Advanced Search


Peer Review

Spherical Harmonics

by Martin Kraus


Overall Numeric Rating:

3.33 stars
Content Quality: 3 stars
Effectiveness: 3 stars
Ease of Use: 4 stars
Reviewed: Jul 11, 2001 by Physics
Overview: 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.
Type of Material: Lecture/Presentation
Identify Major Learning Goals: Three-dimensional visualization of spherical harmonics.
Target Student Population: Upper-Level Undergraduate
Prerequisite Knowledge or Skills: Introductory Quantum Mechanics

Evaluation and Observation

Content Quality

Rating: 3 stars
Strengths: 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.

Concerns: 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

Rating: 3 stars
Strengths: 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.

Concerns: 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

Rating: 4 stars
Strengths: The interface is very intuitive, easy to use.
Concerns: No instructions are given to help on the choice of resolution.

No description of the physics is given.