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  Home > JCE Print > Journal of Chemical Education > Issues > 2007  > July  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Particle-in-a-Box Dynamics
David M. Hanson
Department of Chemistry, State University of New York at Stony Brook, Stony Brook, NY 11794-3400

Theresa Julia Zielinski
Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764

Cover
July 2007
Vol. 84 No. 7
p. 1232
Abstract
The movement of an electron or excitation energy (an exciton) through space from one molecule (or part of a molecule) to another is a common and important process, for example in photosynthesis, in enzyme-mediated redox reactions, as well as in semiconductors. Time-dependent quantum mechanics is needed to understand and describe such phenomena. This activity provides a very simple example of a quantum mechanical description of electron or exciton motion. The document is designed for use in junior–senior level quantum chemistry courses. Successful use of the document requires that students be familiar with expectation values and the physical interpretation given to a wave function, complex numbers and functions, and solution of the time-independent and time-dependent Schrödinger equations for a one-dimensional particle in a box. The document can be used by students in group study either in class or as homework. Instructors can use the document for lecture demonstration and discussion. Clear goals and objectives focus student attention on the key question, electron or exciton motion. Ample questions and exercises further help students master the concepts. The document concludes with a set of reflection questions to help students retain concepts practiced while doing the exercise.

The probability densities for the two particles at T = 0. Students can animate this graph to see how the probability densities change with time.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
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Citation
Hanson, David M.; Zielinski, Theresa Julia. J. Chem. Educ. 2007, 84, 1232.
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Keywords
Computer-Based Learning; Inquiry-Based / Discovery Learning; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Theoretical Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
5/29/2007
6/7/2007
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