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Many, many problems in physics arise from central forces,i.e. forces that depend only on the distance from the source and not on angle. The two most important examples are the gravitational force due to a single spherical or pointlike mass and the electromagnetic force due to a single spherical or pointlike charge. This Paradigm will explore features which all such forces have in common, as well as some special features of the most important examples.
The first week will focus on central forces in classical mechanics especially planetary motion, with emphasis on the importance of the conservation of angular momentum and the concept of the effective potential. The second week will focus on the separation of variables in Schroedinger's equation and related equations in the presence of spherical symmetry, leading to a study of spherical harmonics and angular momentum operators. The culmination of the course will be an in-depth exploration of the quantum theory of the hydrogen atom.
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Last Update 9/24/09, webpage created by Corinne Manogue,
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