exploring the harmonic oscillator wave functions
TRANSCRIPT
1232 JournalofChemicalEducation • Vol.84 No.7 July2007 • www.JCE.DivCHED.org
Information • Textbooks • Media • Resources
Exploring the Harmonic Oscillator Wave Functions
byTheresaJuliaZielinski,DepartmentofChemistry,MedicalTechnology,andPhysics,MonmouthUniversity,WestLongBranch,NJ07764;[email protected]
FileNames:HOExploration11.mcd,HOExploration11.pdf
Keywords:Upper-DivisionUndergraduate;PhysicalChemistry;Computer-BasedLearning;Chemometrics;Mathematics/Sym-bolicMathematics;QuantumChemistry
RequiresMathcad11orhigher
The goal of this document is to have students explore the solutions to the quantum mechanical harmonic oscil-lator Schrödinger equation. Students do this by examining the exponential component, generating the various Hermite polynomials, and then creating the final HO wave functions as a product of a normalization factor, the exponential compo-nent, and a Hermite polynomial. Students also prepare plots of several harmonic oscillator wave functions and probability densities. The plots created with Mathcad provide an effec-tive way for students to draw their own figures and master understanding of the concepts involved. Finally, students can examine the plots at both high and low quantum numbers and
correlate their observations with classical harmonic oscillator predictions of maximum and minimum kinetic energy and maximum probability of the extension of the oscillator.
Plotsof1st,2nd,and4thharmonicoscillatorwavefunctionsdrawnwithMathcad.Studentscangeneratemanysuchplotsandexploretheirproperties.
JCE SymMath: Symbolic Mathematics in Chemistryeditedby
TheresaJuliaZielinskiMonmouthUniversity
WestLongBranch,NJ07764-1898