Energies and Wavefunctions for Several One-Dimensional Potentials©
Ricardo Metz Department of Chemistry Lederle GRT University of Massachusetts Amherst, MA 01003-4510 United States mail to: rbmetz@chemistry.umass.edu
Abstract
This Mathcad module allows students to calculate energies and wavefunctions 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 wavefunctions 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 wavefunction 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 the Variational method. As the approach used is quite general, the module can be readily modified to allow students to calculate wavefunctions and energies of arbitrary one-dimensional potentials. The files are provide here as a zip of several interdependent Mathcad files. The main file is SchEq.mcd. This file contains links to accessory files. You may need to set directory locations in this file in order for the links to work.
Commentary
Editor's Commentary
Keywords
Audiences: Upper-Division Undergraduate, Graduate Education / Research Pedagogies: Computer-Based Learning Domains: Physical Chemistry Topics: Atomic Properties / Structure, Computational Chemistry, Mathematics / Symbolic Mathematics, Quantum Chemistry
Documents
File Name Description Software Type Software Version SchEqMC2000.zip Requires Mathcad2000 or higher Mathcad 2000 SchEqMC2001i.zip requires Mathcad 2001i or higher Mathcad 2001i SchEqAcrobat.zip Archive of Read-Only Documents JCE Subscribers only: name and password or institutional IP number access required.
Citations
Metz, Ricardo J. Chem. Educ. 2004, 81, 157.
Comments to: Ricardo Metz rbmetz@chemistry.umass.edu
©Copyright 2004 Journal of Chemical Education