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  Home > JCE Print > Journal of Chemical Education > Issues > 2004  > January  >
Information, Textbooks, Media, Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Energies and Wave Functions for Several One-Dimensional Potentials
Ricardo Metz
Department of Chemistry, Lederle GRT, University of Massachusetts, Amherst, MA 01003-4510
Cover
January 2004
Vol. 81 No. 1
p. 157
Full Text
This module allows students to calculate energies and wave functions for several one-dimensional potentials. Potentials include: Particle in a finite box, Particle in a box with a barrier, Harmonic oscillator, Morse oscillator, and a Double-minimum potential. Students learn how changing the potential affects the wave functions and their energies by comparing a particle in a box with a particle in a finite box and comparing harmonic and Morse oscillators. In addition, students explore how barriers affect wave function tunneling by looking at two double minima potentials. The potentials used are models for a variety of physical systems, including an O-H stretch vibration and inversion of ammonia. The Schrödinger equation is solved using a particle in a box basis set and variational method. As the approach used is quite general, the module can be readily modified to allow students to calculate wave functions and energies of arbitrary one-dimensional potentials.

Energy as a function of interatomic distance for the harmonic oscillator and Morse potential functions. The energy levels of the harmonic oscillator are shown as solid lines. The energy levels of the Morse oscillator are shown as dashed lines. Screen from Energies and Wave Functions for Several One-Dimensional Potentials.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
*  Contents
*  Download
More Information
*  Citation
 Metz, Ricardo. J. Chem. Educ. 2004 81 157.
*  Keywords
 Atomic Properties / Structure; Computational Chemistry; Computer-Based Learning; Numerical Methods; Physical Chemistry; Quantum Chemistry
*  History
 Created:
Last Updated:		 December 8, 2003
February 18, 2005
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