JCE Online Journal of Chemical Education
 | Subscriptions  | Software Orders  | Support  | Contributors  | Advertisers  | 

JCE Print
   Current Issue
 Previous Issues
 Supplements
 Search JCE Index

JCE Digital Library
   DigiDemos
 QBank
 SymMath
 WebWare

JCE Software
   Latest Releases
 Software & Video
 Downloads
 Support

Only@JCE Online
   JCE Online Store
 JCE HS CLIC
 JCE Discussion Forums
   Biographical Snapshots
 ChemEd Resource Shelf
 Featured Molecules
 Hal's Picks
 Project Chemlab
 Reviewed WWW Sites
 "Web-Ed" Articles

About JCE
   Features
 Publications
 Operations
 Outreach
 Contact Us


  Home > JCE Print > Journal of Chemical Education > Issues > 2000  > April  >
In the Classroom
A Heuristic Derivation of the Linear Harmonic Oscillator Energy Levels
Michael Messina
Department of Chemistry, University of North Carolina at Wilmington, Wilmington, NC 28403-3297
Cover
April 2000
Vol. 77 No. 4
p. 492
Abstract
In this work we present a heuristic derivation for the energy levels of a linear harmonic oscillator that involves only algebra. This derivation offers the instructor a way to rationalize the energy level spectrum of a harmonic oscillator without having to solve the complicated differential equation prescribed by the Schrödinger equation for the harmonic oscillator. This derivation treats the harmonic oscillator as a quasiparticle in a box and yields qualitative results, these being the correct scaling of the energy with quantum number and vibrational frequency, but does not yield the exact result. By comparing the exact result with the result of the heuristic derivation students are introduced to the idea of tunneling in quantum mechanics and how tunneling can effect the energy levels of quantum mechanical systems.
More Information
*  Citation
 Messina, Michael. J. Chem. Educ. 2000 77 492.
*  Keywords
 Computational Chemistry; Physical Chemistry; Quantum Chemistry; Theoretical Chemistry
*  History
 Created:
Last Updated:		 March 2, 2000
April 15, 2005
<< Previous Article Table of Contents Next Article >>
  Home > JCE Print > Journal of Chemical Education > Issues > 2000 > April > Page 492


Subscriptions
 Subscription Info
 Order Forms

JCE HS CLIC

Our Secondary School editors work hard to distill all the JCE materials to produce a fraction of particular interest to high school teachers. We call it CLIC.
 JCE HS CLIC

Contributions Welcome
JCE welcomes your submission
 Contributors' Corner

Advertisers
In recent years we have worked hard to better match our advertisers with our readers. When shopping for chemistry education materials, visit our advertisers' WWW sites first.
 Recent Advertisers

Be An Ambassador
Take JCE along on your outreach missions. Copies of the Journal, guest access to JCE Online, our publications catalog, and more are available for your participants.
 Outreach with JCE

Comments to
jceonline@chem.wisc.edu		 Copyright © Division of Chemical Education, Inc., American Chemical Society.
All rights reserved.