These are two examples of using the quantum mechanics "Hydrogenic" Physlets from the Modern Physics Chapter (Chapter 10) of the book "Physlets: Teaching Physics with Interactive Curricular Material" by Christian and Belloni.

These are flexible applets that display the quantum wavefunctions for the standard quantum problem of the hydrogen (Coulombic) atom. 3D-density plots of wavefunctions (in the x-z plane) can be shown, as well as 2D plots of the radial and angular wavefunctions. Users can input the quantum numbers of the states they wish to investigate. Quantitative values for the wavefunctions can be investigated.

Includes questions about the Hydrogen atom for students to answer.

Type of Material:

Curricular Material (Lecture/Demo or Homework Assignment)

Technical Requirements:

These are examples of the use of Physlets, scriptable building blocks for online physics demonstrations and other learning activities. May not be compatible with Macintosh browsers.

For learning how to use Physlets skillfully, "Physlets: Teaching Physics with Interactive Curricular Material" by W. Christian and M. Belloni is recommended.

Identify Major Learning Goals:

Pictorial description of quantum states to develop "intuition" in students.

Target Student Population:

Sophomore or Junior Modern Physics or Quantum Mechanics Classes. Could be used as supplemental material for more advanced classes.

Prerequisite Knowledge or Skills:

Introduction to Quantum Mechanics

Content Quality

Rating:

Strengths:

Masterfully done. Very clear display of the wavefunctions of the hydrogen atom. Density plot of the wavefunction is attractive and informative. Wavefunctions are shown in several different ways (Density, radial wavefunction, and angular wavefunction). Users can input the quantum numbers as they wish. By mousing over the figure, users can get numerical values for the magnitude of the wavefunction.

Concerns:

Students will need a little more information about what the density plots are showing than is given on the page. (y_{n,l,m}(r) in the x-z plane) This is not a standard graph in most quantum mechanics texts. It is not necessarily clear to what the colors ("phase information") correspond. Using the name "Density Plot", though defined in the text, could be confusing to some students.

The square of the wavefunction, ,y_{n,l,m}(r),^{2} is not shown. This probability density is what is normally shown for images of the hydrogen atom.

Radial plots can be a little cramped for large values of the principal quantum number.

General Comments on Quality: These Physlets give excellent graphical illustrations of some important properties of hydrogenic wave functions.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

Recommended Use(s) for Material: Lecture/Demo, Homework Assignment.

Includes questions regarding the qualitative and quantitative form of the hydrogen atom that enhance the teaching/learning effectiveness of the applets. Allows students to explore the spatial wavefunction properties,
with some guidance.

Concerns:

Use(s) Material is not Suited For: Tutorial (not sufficient explanations of the physical system)

Students will probably need some guidance understanding what they can do with this applet. This is probably because this is more an example for instructors than students.

More unique questions about hydrogenic atoms can be explored using this excellent tool. For example, getting students to look at high N Rydberg states could be useful for thinking about the correspondence principal.

The questions regarding the dependence (or independence) of the wavefunctions on quantum numbers are moot since the wavefunctions are labeled by just the quantum numbers on which they depend.

The questions about the quantitative dependence of the peak in the wavefunction as a function of N will need some previous experience on the part of the student with the hydrogenic wavefunctions.

General Comments on Effectiveness: According to the author, these Physlets "can be used at the beginning of class to introduce topics, during the middle of a topic to test whether students are ready to cover additional material, or at the end of a topic to test students? knowledge of the material just covered." These give good examples of the ways in which this applet can be used. Instructors can build on these examples.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

The usability for students of this applet is excellent. It contains clear, easy to understand controls and input for displaying the wavefunctions. This is a very straightforward applet to use.

The ability to save different plots, and the instructions on how to do so, are a great benefit.

This example can be plugged, as-is, into a course on quantum mechanics. As is true with all Physlets,
the flexibility of this applet allows a wide range of uses, with some work on the part of the instructor.

Concerns:

A simple way to print different plots might be useful. Not Macintosh compatible.

Creative Commons:

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