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Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems

✍ Scribed by A. D. Lewis

Publisher
Springer
Year
1992
Tongue
English
Weight
570 KB
Volume
25
Category
Article
ISSN
0377-9017

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✦ Synopsis

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 ~s derived for the given example, and the corresponding first order asymptotic solution to the reduced Schrrdinger equation is gwen.

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