SymMath Collection  Curator's Commentary  Author Guidelines  Reviewer Guidelines  About JCE SymMath  Contribute!

Energies and Wave Functions for Several One-Dimensional Potentials

Abstract
Downloads
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.

Figure 1. 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

Version	Download
Mathcad 2001i	SchEqMC2001i.zip
Mathcad 2000	SchEqMC2000.zip

Version	Download
Mathcad	SchEq.pdf
Mathcad	SchEq_Accurate.pdf
Mathcad	SchEq_Qualitative.pdf
Mathcad	SchEq_Rules.pdf
Mathcad	SchEq_Variational.pdf

 JCE Subscribers only: Institutional IP number access or name and password required

Commentary

Other Information

Keywords

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Atomic Properties / Structure; Computational Chemistry; Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation