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Introductory Explorations of the Fourier Series by Theresa Julia Zielinski, Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764-1898;
[email protected] File Names: fourier11.mcd and fourier11.pdf Keywords: Audience: Upper-Division Undergraduate. Domain: Physical Chemistry. Pedagogy: Computer-Based Learning. Topics: Chemometrics, Mathematics/Symbolic Mathematics, Quantum Chemistry. Requires Mathcad 11 or higher
The ability to use series expansions effectively is one of the important skills for students in quantum chemistry courses. This Mathcad template enables students to practice this skill using the Fourier series. Students start with the definition of orthonormal functions and then move on to the fundamental equations used in Fourier expansions. Using the Fourier series with odd and even trial functions is introduced by fitting the Fourier series to a simple step function. The study ends with a mastery problem for fitting the Fourier series to an even function. Some previous
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Fourier series of three terms fitted to a step function.
work with the Fourier series or other series in class or through outside readings would be useful as preparation for this exercise. Students also should have basic experience with Mathcad and know the difference between odd and even functions. This exercise serves as a foundation for future work in quantum mechanics where, for example, linear combinations of functions are used to express solutions to the Schrödinger Equation.
Journal of Chemical Education • Vol. 85 No. 12 December 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
