Teaching Qualitative Energy-eigenfunction Shape with Physlets

More than 35 years ago, French and Taylor1 outlined an approach to teach students and teachers alike how to understand “qualitative plots of bound-state wave functions.” They described five fundamental statements based on the quantum-mechanical concepts of probability and energy (total and potential), which could be used to deduce the shape of energy eigenfunctions. Despite these important and easy-to-follow statements, this approach has not been universally adopted in the teaching of quantum mechanics.2 For example, recent studies have shown that students' conceptual understanding of quantum mechanics on all levels is surprisingly lacking3 and that misconceptions are universal,4 including that of the relationship between the potential energy function and the resulting energy eigenfunction shape. At the same time, the teaching of quantum mechanical concepts in introductory physics has become increasingly important given the modern technological applications that are based on quantum theory (e.g., PET scans and MRIs). However, most treatments of quantum theory on the introductory level are cursory at best, leaving students with the impression that quantum mechanics is little more than abstract mathematics (a belief that remains with students in their future courses).