Lesson 1
Addressing Multi-Dimensional Problems - Chladni’s “Acoustics” 4
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Prof. McBride, J. Michael, CHEM 125a, Freshman Organic Chemistry I, Fall 2008, YALE Open Courses: Yale University, Chemistry (Accessed 12/09/2014), http://oyc.yale.edu/chemistry/chem-125a/lecture-9 License: Creative Commons BY-NC-SA After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analogy is pursued by studying the form of wave functions for "hydrogen-like" one-electron atoms. Removing normalizing constants from the formulas for familiar orbitals reveals the underlying simplicity of their shapes.

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