JCE Software, 6B2: Quantum Barrier

Quantum Barrier

David A. Lloyd
Hofstra University, Hempstead, NY 11550

Note:
This program is out of print, but is available for free download by Journal of Chemical Education subscribers.
Go to the download page.

The interaction of a quantum mechanical particle with a potential energy barrier illustrates a number of interesting aspects of quantum behavior, the best known of which is tunneling. This problem has been treated in quantum mechanics texts by Pilar (1), Atkins (2), Davis (3), and Powell and Craseman (4). There is excellent software by Rioux (5) available for many bound-state quantum mechanics problems, but it does not include the barrier problem. Quantum Barrier allows students to interactively discover the effect of particle energy, particle current, barrier height, and barrier thickness on the reflection and transmission coefficients. At the same time the wave function for the particle beam is displayed.
The Quantum Barrier display screen consists of three panels. The lower, or control panel, allows the student to try particle energies up to 1000 eV in 1% increments, and barrier energies up to 400 eV in 5% increments. Thus, the ratio of particle energy to barrier height can be adjusted from 0.025 to 50. The barrier width can be changed from 0.2 to 2.0 Angstrom units, and the particle beam current is adjustable in 1% increments to 1000 mA. In all cases, the mass of the particle is assumed to be the electron rest mass. The use of experimental as opposed to atomic units is intended to give the student an intuitive feeling for the quantities involved.

Screen display from Quantum Barrier.
The center panel depicts the physical situation, using differently colored pixels to represent incident particles as opposed to reflected particles. The speed at which the pixels move across the screen is made approximately proportional to the velocities of the particles they represent. The detector icon in the center panel displays the magnitude of the transmitted current, while the wave function is simultaneously displayed in the upper panel. The imaginary component of the wave function is represented by the thickness of the line drawn on the screen, which allows the phase of the function to be visualized.
Quantum Barrier can be used to explore one or more of the following assignments: Plot the increase in transmission as the particle energy approaches the barrier height. What is the period of the cyclic variation in reflection at particle energies in excess of the barrier energy? How does the phase of the wave function change as the amount of reflection changes? Is transmission more sensitive to barrier height or barrier width? Why does the number of particles in the display decrease with increasing particle energy at constant current?
Hardware and Software Requirements
Programs in this issue of JCE: Software are designed for IBM PC/2, PC, or PC-compatible microcomputers with 640K of RAM and one floppy disk drive. VGA or compatible graphics and PC- or MS-DOS 3.1 or later are also required. (CGA and EGA graphics will not work.)
Literature Cited

Pilar, F. L. Elementary Quantum Mechanics, 2nd ed.; McGraw-Hill: New York, 1990, pp. 73-77.
Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University Press: New York, 1983, pp. 41-44.
Davis, Jr., J. C. Advanced Physical Chemistry, Ronald Press: New York, 1965, pp. 88-93.
Powell, J. L.; Craseman, B. Quantum Mechanics, Addison-Wesley: Reading, MA,1961, pp. 107-109.
Rioux, F. Numerical Solutions for Schrodinger's Equation; J. Chem. Educ.: Software,1990 IIIB (2).

First Published: December 1993
Citation: Lloyd, D. A. . Quantum Barrier J. Chem. Educ. Software 6B2
Keywords: Lecture Aid; Computer Room; Physical; Quantum Chemistry; Tunneling

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Last Updated: April 26, 2001
Created: December 4, 1996 Created by: J. L. Holmes
Comments to: jceonline@chem.wisc.edu

© 1997 Division of Chemical Education, Inc., American Chemical Society. All rights reserved.



Quantum Barrier
David A. Lloyd Hofstra University, Hempstead, NY 11550

Note:	This program is out of print, but is available for free download by Journal of Chemical Education subscribers. Go to the download page.

The interaction of a quantum mechanical particle with a potential energy barrier illustrates a number of interesting aspects of quantum behavior, the best known of which is tunneling. This problem has been treated in quantum mechanics texts by Pilar (1), Atkins (2), Davis (3), and Powell and Craseman (4). There is excellent software by Rioux (5) available for many bound-state quantum mechanics problems, but it does not include the barrier problem. Quantum Barrier allows students to interactively discover the effect of particle energy, particle current, barrier height, and barrier thickness on the reflection and transmission coefficients. At the same time the wave function for the particle beam is displayed. The Quantum Barrier display screen consists of three panels. The lower, or control panel, allows the student to try particle energies up to 1000 eV in 1% increments, and barrier energies up to 400 eV in 5% increments. Thus, the ratio of particle energy to barrier height can be adjusted from 0.025 to 50. The barrier width can be changed from 0.2 to 2.0 Angstrom units, and the particle beam current is adjustable in 1% increments to 1000 mA. In all cases, the mass of the particle is assumed to be the electron rest mass. The use of experimental as opposed to atomic units is intended to give the student an intuitive feeling for the quantities involved. Screen display from Quantum Barrier. The center panel depicts the physical situation, using differently colored pixels to represent incident particles as opposed to reflected particles. The speed at which the pixels move across the screen is made approximately proportional to the velocities of the particles they represent. The detector icon in the center panel displays the magnitude of the transmitted current, while the wave function is simultaneously displayed in the upper panel. The imaginary component of the wave function is represented by the thickness of the line drawn on the screen, which allows the phase of the function to be visualized. Quantum Barrier can be used to explore one or more of the following assignments: Plot the increase in transmission as the particle energy approaches the barrier height. What is the period of the cyclic variation in reflection at particle energies in excess of the barrier energy? How does the phase of the wave function change as the amount of reflection changes? Is transmission more sensitive to barrier height or barrier width? Why does the number of particles in the display decrease with increasing particle energy at constant current? Hardware and Software Requirements Programs in this issue of JCE: Software are designed for IBM PC/2, PC, or PC-compatible microcomputers with 640K of RAM and one floppy disk drive. VGA or compatible graphics and PC- or MS-DOS 3.1 or later are also required. (CGA and EGA graphics will not work.) Literature Cited Pilar, F. L. Elementary Quantum Mechanics, 2nd ed.; McGraw-Hill: New York, 1990, pp. 73-77. Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University Press: New York, 1983, pp. 41-44. Davis, Jr., J. C. Advanced Physical Chemistry, Ronald Press: New York, 1965, pp. 88-93. Powell, J. L.; Craseman, B. Quantum Mechanics, Addison-Wesley: Reading, MA,1961, pp. 107-109. Rioux, F. Numerical Solutions for Schrodinger's Equation; J. Chem. Educ.: Software,1990 IIIB (2).


News \| Issues \| CD-ROM / Video \| Find It! \| Technical Support \| For Authors
JCE Online \| Journal \| Software \| Internet \| Happenings \| About JCE \| Contact JCE

Last Updated: April 26, 2001 Created: December 4, 1996	Created by: J. L. Holmes Comments to: jceonline@chem.wisc.edu

© 1997 Division of Chemical Education, Inc., American Chemical Society. All rights reserved.