Teaching Qualitative Energy-eigenfunction Shape with Physlets

Mario Belloni (Davidson College)
Wolfgang Christian (Davidson College)
Anne J. Cox (Eckerd College)

The most fundamental construct of time-independent quantum mechanics is that of the eigenfunction that describes energy eigenstates. One of the most important questions in quantum mechanics is why does an energy eigenfunction have the shape that it does? In this paper we revisit and update a classic paper by describing several simple, yet accurate, concepts for determining energy eigenfunction shape coupled with computer-based visualization. Along the way, we shall see which concepts we can “borrow” from classical physics and which ones we must “discard.” To help visualize energy eigenfunctions, we have created computer-based Physlet exercises which can be used as in-class, tutorial or laboratory exercises.

The materials are broken up into three parts:

  1. Overview: Contains the overall description of the materials and their design features.
  2. QM Tutorial: Contains text that describes how to analyze energy eigenfunction shape.
  3. Exercises: Contain the Classical, Quantum Mechanical, Design Your Own Well, and Other exercises.

In addition you may download two versions of the paper, "Teaching Qualitative Energy-eigenfunction Shape with Physlets."  The short version has been submitted to TPT and does not contain the tutorial on analyzing energy eigenstate shape.  The long version has a detailed discussion of analyzing energy eigenstate shape.  You can get a pdf below by selecting a link below"

Download pdf of short version

Download pdf of long version

This work is supported by the National Science Foundation (DUE-0442581).