Energies and Wave Functions for Several One-Dimensional Potentials
Ricardo Metz
Department of Chemistry, Lederle GRT, University of Massachusetts, Amherst, MA 01003-4510
Abstract
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Commentary
More Information: Keywords, JCE Citation
Abstract
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.
Downloads
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SchEqMC2001i.zip |
compressed archive.zip (contains Mathcad.mcd) |
173 KB |
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Fully interactive with Mathcad 2001i: SchEq.mcd, SchEq_Accurate.mcd, SchEq_Qualitative.mcd, SchEq_Rules.mcd, SchEq_Variational.mcd
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SchEqMC2000.zip |
compressed archive.zip (contains Mathcad.mcd) |
56.7 KB |
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Fully interactive with Mathcad 2000: SchEq2000.mcd, SchEq_Accurate2000.mcd, SchEq_Qualitative2000.mcd, SchEq_Rules2000.mcd, SchEq_Variational2000.mcd
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SchEq.pdf
SchEq_Accurate.pdf
SchEq_Qualitative.pdf
SchEq_Rules.pdf
SchEq_Variational.pdf |
Acrobat.pdf |
159 KB
41.6 KB
69.6 KB
41.8 KB
96.1 KB |
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Non-interactive derived from Mathcad 2001i files. |
JCE Subscribers only: Institutional IP number access or name and password required
Commentary
Editor's Commentary
Other Information
KeywordsComputational Chemistry; Computer-Based Learning; Numerical Methods; Physical Chemistry; Quantum Chemistry JCE Citation
Metz, Ricardo. J. Chem. Educ. 2004, 81, 157.
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