Visualizing Particle-in-a-Box Wavefunctions
Edmund L. Tisko
Department of Chemistry, University of Nebraska at Omaha, Omaha, NB 68182
etisko@unomaha.edu
Translated to Mathematica by:
Alex Grushaw
Department of Chemistry, Biochemistry, and Physics, Rider University, Lawrenceville, NJ 08648
Abstract
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Abstract
Using the built-in differential equation solvers and graphical capabilities of Mathcad, students can visualize the wavefunctions of the particle-in-a-box potential. By applying the mathematical requirements of the wavefunction, the particle in a box is seen to have quantized energies. By plotting possible solutions, students are able to visualize the consequences of requiring the wavefunction to be continuous. Also, the step potential and barrier potential can be examined, thus allowing students to see how requiring the wavefunction to be finite results in the quantum mechanical phenomenon of tunneling.
The instructor notes include Mathcad graphics illustrating some of the peculiar features of the simple particle in a box, the step potential, and the double-well barrier potential.
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Keywords
Computational Chemistry, Physical Chemistry, Quantum Chemistry, Theoretical Chemistry
JCE Citation
Tisko, E. L. J. Chem. Educ. 2003, 80, 581.
Grushaw, A.. J. Chem. Educ. 2005, 82, 175.
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