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Visualizing Plane Wave Partial Wave Expansions
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In mathematical physics and introductory quantum mechanics classes I have found that students are puzzled by the formidable-looking partial-wave expansion of plane waves in non-Cartesian coordinate systems, such as spherical polar coordinates. Such expansions are vital steps when solving scattering problems in both classical and quantal physics. There are two main pedagogical reasons for students' bewilderment: first, the complexity of deriving the formulas and, second, the nonintuitive nature of the resulting formulas, which have a plethora of Bessel functions and Legendre polynomials intertwined like snakes in a horror movie. I have recently given a concise derivation of the plane wave partial wave expansion that is readily accessible to mathematics and physics students after they have been introduced to the elementary properties of Bessel and Legendre functions. The purpose of the present article is to show how Mathematica can be used to visualize these partial-wave formulas.
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| Thompson.code.nb (163.5 KB) - Mathematica Notebook |
Files specific to Mathematica 2.2 version:
| | Thompson.code.ma (127.9 KB) - Mathematica Notebook 2.2 or older |
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