Exploring the Uncertainty Principle©
Franklin M.C. Chen
Department of Chemistry
University of Wisconsin-Green Bay
Green Bay, WI 54311-7001
United States
mail to: chenf@uwgb.edu

This Mathcad template uses two Gaussian functions to guide students in exploring uncertainty principle. The standard deviations of Gaussian functions provide measures of position operator uncertainty. Students are asked to build a linear combination of orthogonal particle-in-a-box eigenfunctions to represent Gaussian functions. It leaves students to discover that a Gaussian function with smaller standard deviation requires more eigenfunctions to build than that with a larger standard deviation. The magnitude of momentum uncertainty is related to both the number of eigenfunctions and the eigennumbers of these eigenfunctions. Through this exercise, students are guided to discover the relationship between position and momentum uncertainty to a given wavefunction.
Editor's Commentary
Audiences: Upper-Division Undergraduate
Domains: Physical Chemistry
Topics: Mathematics / Symbolic Mathematics, Quantum Chemistry
File NameDescriptionSoftware TypeSoftware Version
UncertaintyPrinciple.pdf Read-Only Document
TheUncertaintyPrinciple.mcd JCE Mathcad Computational Document. Mathcad
JCE JCE Subscribers only: name and password or institutional IP number access required.
Chen, F. M. C. J. Chem. Educ. 2005, 82, 1101
Comments to: Chen, Franklin
©Copyright 2005 Journal of Chemical Education