Harmonic Oscillator (Worksheet)

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With this document students can explore the solutions to the quantum mechanical harmonic oscillator Schrodinger equation by (1) examining the exponential component, (2) generating and examining various Hermite polynomials, and (3) combining these to see that the final HO wavefunctions as a product of a normalization factor, the exponential component, and a Hermite polynomial. Students are also led to prepare graphs of several harmonic oscillator solutions and the corresponding probability density functions. They can also explore how the probability density changes as the quantum number increases to a large number. This gives insight into the Correspondance Principle. Using Mathcad is an effective way for them to draw their own figures and master understanding of the concepts involved. Below are the JCE citation, the Mathcad document requiring Mathcad 11 or higher (JCE personal or University subscription required), and the Acrobat file showing the details of the Mathcad document (no subscription to JCE required).

Download Site: http://www.jce.divched.org/JCEDLib/SymMath/collection/article.php?id=54
Acrobat file: http://www.jce.divched.org/JCEDLib/SymMath/collection/054/HOExploration11.pdf

References

Zielinski, T. J., J. Chem. Educ. 2007, 84, 1232.