W. Tandy Grubbs
Fourier Transforms of Molecular Vibrations JCE
W. Tandy Grubbs, Stetson University
This series of three Mathcad instructional documents permits students to explore the relationship between the time and frequency representations of vibrational motion in simple diatomic molecules. Exercises included throughout and at the end of each document allow students to practice the numerical methods and further investigate how bond anharmonicity and vibrational damping affect the frequency spectrum.
The Diffusion Game - Using Symbolic Mathematics Software to Play the Game on a Large Scale JCE
W. Tandy Grubbs, Stetson University
A Mathcad instructional document that allows students to explore the diffusion. The goal of the activites in this document is to observe how the statistical 'microscopic' behavior of individual particles ultimately determines a certain 'macroscopic' behavior in a large system. The document provides simulations using the random number generator of Mathcad The outcome of the simulations are analyzed within the context of equilibrium and non-equilibrium states, entropy maximization, and Fick's law of diffusion, reinforcing one's understanding of the microscopic origin of these phenomena.
Variational Methods Applied to the Particle in the Box JCE
W. Tandy Grubbs, Stetson University
A Mathcad instructional document that allows students to explore the variational method. The variational method is used here to estimate the energy levels of the particle in a one-dimensional box, where exact expressions are available for the energies and wave functions. By practicing the variational method on a known system, students explore the factors that govern the accuracy of the estimated energy and thereby gain an appreciation and confidence in the variational method that is difficult to obtain in any other fashion. Exercises are included that allow students to try the variational method using a wide range of trial functions.