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  Home > JCE Print > Journal of Chemical Education > Issues > 2006  > November  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Symbolic Math Approach To Solve Particle-in-the-Box and H-Atom Problems
Todd M. Hamilton
Department of Chemistry, Georgetown College, Georgetown, KY 40324
Cover
November 2006
Vol. 83 No. 11
p. 1726
Abstract
The Schrödinger equation can be solved exactly for the hydrogen atom. In this assignment, students will solve the equation symbolically using Mathcad's derivatives feature. The result is an expression for the energy levels of the hydrogen atom. Students will also prove that the radial part of the wave function is normalized and explore the concept of an orbital. This exercise is intended for junior-level students who have been introduced to quantum mechanics. Students should be able to solve the particle-in-the-box problem and plot the wave functions for the first several energy levels and have some experience with derivatives and integrals in Mathcad.

Probability density for radial part of the hydrogen 1s wave function.

Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
*
Citation
Hamilton, Todd M. J. Chem. Educ. 2006 83 1726.
*
Keywords
Computer-Based Learning; Hydrogen; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
9/19/2006
9/20/2006
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