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The Chemical Educator
ISSN: 1430-4171 (electronic version)
Abstract Volume 15
(2010) pp 134-140
Thinking Outside the (Particle in a) Box: Tunneling, Uncertainty and Dimensional Analysis
Nathaniel C. Blank, Kate Clemons, Ryan Crowdis, Carla Estridge, Monica Foster, Stacey Gash, Brandon Gish, Bradley Gollihue, Cameron Henzman, Deysi Hernandez, Talha Ijaz, Ashley Ivey, Jacob Jones, Andrea Loveless, Sloan Roberts, Tyla Sauley, Ellyn Velasco, Chase Wilson, Mary M. Blackburn, Henry E. Montgomery, Jr.*
Chemistry Program, Centre
College, 600 West Walnut Street, Danville, KY 40422-1394; ed.montgomery@centre.edu
Received
November 10, 2008. Accepted January 14,
2010.
Published: 3 March 2010
Abstract. We investigate the problem of a quantum particle confined in a finite one-dimensional square well. The eigenvalues and eigenfunctions are found using a computer algebra system to solve the equations that result from matching the logarithmic derivatives at the well boundaries. The wavefunctions are used to investigate the relation of well depth to tunneling and to the Heisenberg uncertainty relations. We demonstrate how dimensional analysis can be used to locate the minimum uncertainty for a given confining potential.
Key Words: In the Classroom; physical chemistry; quantum
(*) Corresponding author. (E-mail: ed.montgomery@centre.edu)
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