Symbolic Math Approach To Solve Particle-in-the-Box and H-Atom Problems©
Todd M. Hamilton
Department of Chemistry
Georgetown College
Georgetown, KY 40324
United States
mail to: Todd_Hamilton@georgetowncollege.edu

The Schrödinger equation can be solved exactly for the hydrogen atom. After practicing with the particle-in-a-box problem, students solve the H atom symbolically using the derivatives feature in MathCad. The result is an expression for the energy levels of the hydrogen atom. Students will also prove that the radial part of the wavefunction is normalized and explore the concept of an orbital. This exercise is intended for junior-level students who have been introduced to quantum mechanics, particularly the particle-in-a-box. Students should also have some experience with derivatives and integrals in Mathcad.
Editor's Commentary
Audiences: Upper-Division Undergraduate
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Mathematics / Symbolic Mathematics, Quantum Chemistry
Elements: Hydrogen
File NameDescriptionSoftware TypeSoftware Version
H_AtomInstructor.mcd JCE Mathcad Computational Document, Instructor Version. Mathcad 12
H_AtomStudent.pdf Read-Only Document, Student Version.
H_AtomInstructor.pdf Read-Only Document, Instructor Version.
H_AtomStudent.mcd JCE Mathcad Computational Document, Student Version. Mathcad 12
JCE JCE Subscribers only: name and password or institutional IP number access required.
Hamilton, Todd M. J. Chem. Educ. 2006 83, 1726.
Comments to: Todd_Hamilton@georgetowncollege.edu
©Copyright 2006 Journal of Chemical Education