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Please use this identifier to cite or link to this item: http://hdl.handle.net/1974/202

Title: Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
Authors: Lewis, Andrew D.

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1991a_letter.pdf484.62 kBAdobe PDFView/Open
Issue Date: 1992
Publisher: D. Reidel
Citation: Letters in Mathematical Physics 25(3), pages 189-201, 1992
Abstract: In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple interpretation in terms of the dynamics near the singularity of the potential. Lagrangian submanifolds also arise when seeking asymptotic solutions to certain partial differential equations with a large parameter. In determining such solutions, an operator between half densities on the Lagrangian submanifold and half densities on the configuration space is computed. This operator is derived for the given example, and the corresponding first order asymptotic solution to the reduced Schrödinger equation is given.
URI: http://hdl.handle.net/1974/202
Appears in Collections:Department of Mathematics and Statistics: Dr. Andrew D. Lewis

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