Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
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Authors
Lewis, Andrew D.
Date
1992
Type
journal article
Language
en
Keyword
Alternative Title
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.
Description
Citation
Letters in Mathematical Physics 25(3), pages 189-201, 1992
Publisher
D. Reidel