Particle in a Box
Energies and Wavefunctions for Several One-Dimensional Potentials JCE
Ricardo Metz, University of Massachusetts
This Mathcad module allows calculation of energies and wavefunctions for several one-dimensional potentials: Particle in a finite box, Particle in a box with a barrier, Harmonic oscillator, Morse oscillator, and a Double-minimum potential, comparison of the wavefunctions and their energies, and how barriers affect wavefunction tunneling by looking at two double minima potentials.Aa particle in a box basis set and the Variational method are used.
Particle-in-a-Box Dynamics JCE
Theresa Julia Zielinski, Monmouth University
David M. Hanson, State University of New York at Stony Brook
This Mathcad document explores the time-dependent quantum mechanics for a particle-in-a-box using guided inquiry and the animation tools of the software.
Potential Barriers and Tunneling JCE
Mark David Ellison, Wittenberg University
A document to provide students with the opportunity to develop their understanding of the behavior of particles in the presence of finite barriers. Color enhancement of the wave function and probability density plots clearly delineate the different regions and makes clear what has happened.Also Scanning Tunneling Microscopy is examined followed by applications of the tunneling concept to chemical reactions.
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.
Visualizing Particle-in-a-Box Wavefunctions using Mathcad JCE
Edmund L. Tisko, University of Nebraska at Omaha
Using the built-in differential equation solvers and the graphical capabilities of Mathcad, students can visualize the wavefunctions of the particle-in-a-box potential. The document examines bound states and tunneling using the particle in a box, step potential and double well potential.