Getting acquainted with gears and wheels – quantum mechanically

Abstract

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. For a pair of wheels or gears with positive coupling, i.e., without slip or play, there are rules of engagement that have some interesting consequences when their dynamics is treated quantum mechanically. We will illustrate the principal ideas involved here with the help of an elementary, basically a textbook exercise whose solution, however, is not only interesting, but may also be re-interpreted rather creatively. Possible relevance of this simple exercise to the incredible, ever-shrinking world of the nano (1 nm = 10^-9 m) is pointed out.