Deeper look at student learning of quantum mechanics: The case of tunneling

(Some reference links may require a separate subscription.)

1. B. Ambrose, Ph.D. thesis, University of Washington, 1999.
2. L. Bao, Ph.D. thesis, University of Maryland, 1999.
3. J. T. Morgan, M. C. Wittmann, and J. R. Thompson, in 2003 Physics Education Research Conference Proceedings, edited by S. Franklin, K. Cummings, and J. Marx (AIP, Melville, NY, 2004).
4. M. C. Wittmann, J. T. Morgan, and L. Bao, Addressing student models of energy loss in quantum tunneling, Eur. J. Phys. 26, 939 (2005) [INSPEC].
5. J. Falk, M.S. thesis, Uppsala University, 2004.
6. D. Domert, C. Linder, and Å. Ingerman, Probability as a conceptual hurdle to understanding one-dimensional quantum scattering and tunneling, Eur. J. Phys. 26, 47 (2005).
7. S. B. McKagan and C. E. Wieman, in 2005 Physics Education Research Conference Proceedings, Exploring Student Understanding of Energy through the Quantum Mechanics Conceptual Survey, edited by P. Heron, L. McCullough, and J. Marx (AIP, New York, 2006).
8. S. B. McKagan, K. K. Perkins, and C. E. Wieman, in 2006 Physics Education Research Conference Proceedings, Reforming a large lecture modern physics course for engineering majors using a PER-based design, edited by L. McCullough, P. Heron, and L. Hsu (AIP, New York, 2007).
9. Course materials available online at http://per.colorado.edu/modern.
10. D. Hestenes, Toward a modeling theory of physics instruction, Am. J. Phys. 55, 440 (1987) [SPIN][INSPEC][ADS].
11. A. P. French and E. F. Taylor, An Introduction to Quantum Physics (Norton, New York, 1978).
12. A. Goldberg, H. M. Schey, and J. L. Schwartz, Computer-generated motion pictures of one-dimensional quantum-mechanical transmission and reflection phenomena, Am. J. Phys. 35, 177 (1967) [SPIN].
13. It is linguistically awkward to speak of the potential energy “inside the barrier” since the potential energy is the barrier, but it is important to be explicit, as many students do not recognize the equivalence of potential energy and barrier.
14. L. Viennot, Spontaneous reasoning in elementary dynamics, Eur. J. Sci. Educ. 1, 205 (1979).
15. D. E. Trowbridge and L. C. McDermott, Investigation of student understanding of the concept of velocity in one dimension, Am. J. Phys. 48, 1020 (1980) [SPIN][INSPEC].
16. D. E. Trowbridge and L. C. McDermott, Investigation of student understanding of the concept of acceleration in one dimension, Am. J. Phys. 49, 242 (1981) [SPIN][INSPEC].
17. J. Clement, Students' preconceptions in introductory mechanics, Am. J. Phys. 50, 66 (1982) [SPIN][INSPEC].
18. I. A. Halloun and D. Hestenes, Common sense concepts about motion, Am. J. Phys. 53, 1056 (1985) [SPIN][INSPEC].
19. I. Galili and V. Bar, Motion implies force: Where to expect vestiges of the misconception? Int. J. Sci. Educ. 14, 63 (1992).
20. D. T. Brookes and E. Etkina, in 2005 Physics Education Research Conference Proceedings, edited by P. Heron, L. McCullough, and J. Marx (AIP, Melville, NY, 2006).
21. D. T. Brookes, Ph.D. thesis, Rutgers University, 2006.
22. M. C. Wittmann, R. N. Steinberg, E. F. Redish, and University of Maryland Physics Education Research Group, Activity-Based Tutorials Modern Physics (Wiley, New York, 2005), Vol. 2.
23. R. Harris, Nonclassical Physics, 1st ed. (Pearson, Menlo Park, 1998).
24. R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (Wiley, New York, 1985).
25. The simulation discussed in the next section uses both labels to help students relate the more correct term to the term that is more commonly used in textbooks.
26. http://phet.colorado.edu/tunneling.
27. http://phet.colorado.edu.
28. J. R. Hiller, I. D. Johnson, and D. F. Styer, Quantum Mechanics Simulations: The Consortium for Upper-Level Physics Software (Wiley, New York, 1995).
29. B. Thaller, Visual Quantum Mechanics (Springer, New York, 2000).
30. M. Belloni, W. Christian, and A. J. Cox, Physlet Quantum Physics: An Interactive Introduction (Pearson Prentice Hall, Upper Saddle River, NJ, 2006).
31. http://web.phys.ksu.edu/vqm.
32. http://www.quantum-physics.polytechnique.fr.
33. http://falstad.com/mathphysics.html.
34. S. B. McKagan, K. K. Perkins, M. Dubson, C. Malley, S. Reid, R. LeMaster, and C. E. Wieman, Developing and researching PhET simulations for teaching quantum mechanics, Am. J. Phys. 76, 406 (2008).
35. W. K. Adams, S. Reid, R. LeMaster, S. B. McKagan, K. K. Perkins, and C. E. Wieman, A study of educational simulations Part I: engagement and learning, J. Interact. Learn. Res. 19, 397 (2008).
36. While the transformed curriculum was designed specifically for engineering majors, it was used in the physics majors’ course in the semester following this study. This course was not included in the study due to lack of time. Anecdotal observations suggest that the physics majors tended to pick up on things faster, so that the prevalence of many of the difficulties cited here was somewhat less for them, but the qualitative results of this study were not significantly different for this population.
37. http://per.colorado.edu/QMCS.
38. S. B. McKagan, K. K. Perkins, and C. E. Wieman (unpublished).
39. A. Elby, What students’ learning of representations tells us about constructivism, J. Math. Behav. 19, 481 (2000).
40. R. W. Gurney and E. U. Condon, Quantum mechanics and radioactive disintegration, Phys. Rev. 33, 127 (1929) [ADS].
41. J. B. Pethica and R. Egdell, Surface science: The insulator uncovered, Nature (London) 414, 27 (2001) [CAS].
42. D. J. Griffiths, Quantum Mechanics, 2nd ed. (Pearson, Upper Saddle River, 2005).
43. J. R. Taylor, C. D. Zafiratos, and M. A. Dubson, Modern Physics for Scientists and Engineers, 2nd ed. (Pearson Prentice Hall, Upper Saddle River, 2004).
44. K. Krane, Modern Physics, 2nd ed. (Wiley, New York, 1996).
45. R. A. Serway, C. J. Moses, and C. A. Moyer, Modern Physics, 1st ed. (Saunders, Philadelphia, 2005).
46. H. C. Ohanian, Modern Physics, 2nd ed. (Prentice, Englewood Cliffs, NJ, 1995).
47. R. Knight, Physics for Scientists and Engineers, 1st ed. (Pearson, San Francisco, 2004).
48. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics (Wiley, New York, 1977).
49. R. Shankar, Principles of Quantum Mechanics (Springer, New York, 1994).
50. J. Lande, T. Norsen, and S. B. McKagan, How and why to think about scattering in terms of wave packets instead of plane waves arXiv:0808.3566.
51. http://phet.colorado.edu/qwi.
52. The Activity-Based Tutorials (Ref. [22]), one of which we adapted for use in our curriculum, also include several exercises for building up the idea of potential-energy graphs through laboratory activities with carts on magnetic tracks. We did not use these activities due to lack of time and lack of a laboratory section in our course and because we were more interested in helping students understand potential-energy diagrams for real quantum systems than for classical systems. However, our research indicates that such an approach could be useful if connections are made between these classical examples and examples of systems where quantum mechanics applies.