Teaching Time Development
in Quantum Mechanics

This page written by Dan Styer, Oberlin College Physics Department;
last updated 24 October 1997.

A paper contributed to the meeting of the Ohio Section of the American Physical Society
at Miami University, Oxford, Ohio, 11 October 1997.



Attention devoted to time development in a quantum mechanics course makes the subject less formal and more tangible. This can be done effectively through computer simulation or through analytic problems. Six specific problems are suggested, including an Ehrenfest treatment of the simple harmonic oscillator, displaced energy states of the simple harmonic oscillator, and quantal recurrence in the Coulomb problem.

Why do students find quantum mechanics so hard?

Time development through computer simulation

I shamelessly recommend my own award-winning simulation program Quantum mechanical time development (QMTime), published as part of J.R. Hiller, I.D. Johnston, and D.F. Styer, Quantum Mechanics Simulations (Wiley, New York, 1995).

Time development through analytic problems

Any of the six topics below can be worked into an assignment for students at the junior level. (I plan to provide downloadable TeX source for such assignments . . . but that's still under construction.)

A fundamental misconception

Even the best of us make errors. Linus Pauling and Roger Hayward, The Architecture of Molecules (Freeman, San Francisco, 1964), plates 2 and 3, suggest that in quantum mechanics particles really are tiny classical entities with definite values for both position and momentum, but that they move in a blur, too quickly to be pinned down.

Similarly, the video Eureka! The Conduction of Heat "illustrates how electrons whiz so quickly around the nucleus that they appear to form layers". (See the 1997-98 physics catalog from "Films for the Humanities and Sciences", 1-800-257-5126, page 3.) [This reference was brought to my attention through a comment at my Miami University talk by Professor Joseph West of Wabash College.]

In both cases powerful teaching tools (beautiful visualization and dynamic video, respectively) are used to effectively propagate a misconception. It is hard to see how such a picture could give rise to quantal interference. And it leaves completely open the question of how much time development is due to this postulated blur and how much is encompassed by regular quantal time evolution.