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Potential Barriers and Tunneling

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Abstract

This document provides students with the opportunity to develop their understanding of the behavior of particles in the presence of finite barriers. Students first examine the behavior of a particle and the wave function before, during, and after interacting with the barrier (Figure 1). Color enhancement of the wave function plot clearly delineates the different regions and makes clear what has happened to the wavefunction associated with the particle. Both real and imaginary parts of the wave function are examined. Finally the probability distribution function is plotted. Next Scanning Tunneling Microscopy is examined, followed by applications of the tunneling concept to chemical reactions. Guided inquiry questions promote student interaction with the materials and active learning. The document would be appropriate to use in junior and senior level chemistry courses as well as in a first quantum chemistry course in graduate programs.

Figure 1. The real part of the wave function for a particle in a box with a finite barrier as a function of the location of the particle in the box, (inside the box, the barrier, and outside the box regions are shown from left to right in the image)

Downloads

Version	Download
Mathcad 2001i	QuantumMechanicalTunneling2001i.mcd
Mathcad 8	QuantumMechanicalTunneling8.mcd

Version	Download
Mathcad	QuantumMechanicalTunneling.pdf

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Keywords

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Mathematics / Symbolic Mathematics; Quantum Chemistry; Surface Science;

JCE Citation