Proposal for the Associated Colleges of the South Teaching with Technology Fellows Program

Title: Using Physlets and Just-in-Time Teaching in Quantum Mechanics

Applicants: Mario Belloni (MB)[1], Larry Cain (LC)[2], and Wolfgang Christian (WC)[3]

Physics Department, Davidson College

Abstract: We propose to develop curricular material in support of a one-semester, intermediate course in quantum mechanics. This curricular material uses the Just-in-Time Teaching (JiTT) technique and, where applicable, Physlets to actively engage students outside of the classroom to enhance their in-class experience. Twenty such JiTT exercises will be developed stressing visualization of quantum mechanical concepts with the goal of achieving better student understanding of these concepts.

Physlets and JiTT

Physlets—“Physics applets” written by WC—are small, flexible Java applets that can be used in a wide variety of WWW applications [Christian and Belloni, 2000]. Physlet animations show simple representations of physical and non-physical situations[4] and standard VCR-type buttons allow students to pause, step forward, step back and reset the animations for analysis. The animations are also simple for instructors to create and control with JavaScript. Physlets can run on almost any platform (currently not on the Macintosh) and are free for noncommercial use from the Davidson College WebPhysics server.

The goal of Just-in-Time Teaching [Novak, Patterson, Gavrin, and Christian, 1999] is to actively engage students outside of the classroom (WWW) to enhance their in-class experience. This is primarily accomplished with WarmUps. WarmUps are web-based pre-instruction exercises that are assigned and due before the beginning of the next class period. Students submit their answers to the instructor over the web via a form that appears on the assignment’s web page. The instructor receives the student submissions, and armed with this information, the instructor crafts a lecture around these responses based on students’ needs. Students are both better prepared for class and better motivated to learn the correct answers and justifications.

Student Learning of Quantum Mechanics

Learning quantum mechanics is difficult for many students. There are three reasons[5] for this:

· Quantum mechanics is not like classical mechanics (uncertainty versus determinism).

· Quantum mechanics is one level (at least) divorced from the world we live in.

· Quantum mechanics is inherently mathematical.

The exercises we will develop will be geared to addressing these difficulties. Daily JiTT exercises (WarmUps) will help students be better prepared for class. Students prepared for class by doing these targeted exercises are more motivated to understand the material presented and will actively participate in class. Given how difficult quantum mechanics is to comprehend, this preparation and motivation is crucial. In addition, the visual nature of Physlet exercises will aid students in understanding both the concepts and the mathematics behind quantum theory. While the Physlets can be scripted to handle the mathematics, their power is best harnessed in the graphical representation of the mathematics.

Sample Exercises

The curricular material we will develop will use the Just-in-Time Teaching (JiTT) technique and Physlets. Twenty such exercises will be developed stressing visualization of quantum mechanical concepts with the goal of achieving better student understanding of these concepts. WC has added (and continues to add) new features to Physlets: 3d visualization, numeric integration, one- and two-dimensional fast Fourier Transforms (FFTs), and quantum mechanical time development. We will take advantage of these new features to write innovative curricular material for quantum mechanics. Several possible exercises are listed below:

· Correspondence between classical and quantum physics.

· Interpretation of the wave function.

· Infinite square well.

· Time-dependent wave functions.

· Superposition of states.

· Time-dependent superposition.

· Expectation values.

· Free-particle wave functions in position and momentum space.

· Finite square well.

· Quantum harmonic oscillator.

· Coulomb potential (“Hydrogenic” atoms).

Integration into the Curriculum

In many ways, the Physlet and the JiTT approaches have already been assimilated into the lower-division courses taught by the Physics Department at Davidson College. Physlets have been used by MB, LC, and WC in their introductory physics classes as Just-in-Time Teaching pre-class and pre-lab assignments, as in-class demonstrations, and as traditional homework assignments, and used in the modern physics class as laboratory exercises. MB is currently teaching the intermediatelevel course in quantum mechanics and will continue to do so for the next two years. As a consequence, he will use the materials developed from this grant during fall 2001 and fall 2002 in his Physics 360 course.

Expertise of the Applicants

MB has already used the JiTT technique in his introductory physics and junior-level electromagnetic theory classes and has developed original material for these courses. LC has taught the quantum mechanics course at Davidson numerous times and in spring 2002 will teach the electromagnetic theory course using MB’s JiTT and Physlet exercises. LC and MB will use their experiences in teaching quantum mechanics to develop JiTT and Physlet exercises that will aid students. WC is the author of the applets (the Physlets) we will be using. He will add functionality to the applets, as necessary, to support the curricular materials developed by MB and LC.

Institutional and Technical Support

The Physics Department maintains its own servers and therefore server space and server access is not an issue. All three of us have office computers powerful enough to complete this project. In addition, the College supports our preferred authoring tools, such as Microsoft FrontPage.

Dissemination and Evaluation

webphysics.davidson.edu. Department chairs will be contacted with this information and asked to distribute the web address to their colleagues. In addition, MB, LC, and WC have given numerous invited and contributed talks at local and national meetings of the American Association of Physics Teachers (AAPT) regarding Physlets and physics pedagogy and will disseminate the curricular materials developed in this manner. We will evaluate our materials by administering pre- and post-tests developed by E. Redish, R. Steinberg, and M. Wittmann[6] and, where necessary, create our own pre- and post-tests. The pre- and post-tests will involve qualitative questions in the areas where students have difficulties (such as matching wave functions with quantum wells and barriers). We will compare the pre- and post-test results to evaluate the effectiveness of our materials.

Bibliography

Just-in-Time Teaching: Blending Active Learning with Web Technology, G. Novak, E. Patterson, A. Gavrin, and W. Christian, Prentice Hall, Upper Saddle River, NJ, 1999.

Physlets: Teaching Physics with Interactive Curricular Material, W. Christian and M. Belloni, Prentice Hall, Upper Saddle River, NJ, 2000.

Understanding Quantum Physics: A Users Manual, M. Morrison, Prentice Hall, Upper Saddle River, NJ, 1990.

Hyperlink References

http://webphysics.davidson.edu/physletprob, the WWW version of the curricular and reference material that accompanies: Physlets: Teaching with Interactive Curricular Material, W. Christian and M. Belloni, Prentice Hall, 2000.

http://webphysics.davidson.edu/applets/applets.html, the Physlets website.

http://webphysics.davidson.edu/mjb/enm/phys-350daily00.html, spring 2000 web page with the Just-in-Time Teaching assignments for the course Physics 350 (Electromagnetic Theory).

[4]See for example, Chapters 7-10 in Physlets: Teaching Physics with Interactive Curricular Material or the online version at: http://webphysics.davidson.edu/physletprob.

[5]This discussion parallels Michael Morrison in Understanding Quantum Physics, page 12.

[6]E.F. Redish, R.N. Steinberg, and M.C. Wittmann, “A New Model Course in Applied Quantum Physics,” http://www.physics.umd.edu/perg/qm/qmcourse/welcome.htm.