caa a22 4500 469099887 CHVBK 20180323133041.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF00406547 doi (NATIONALLICENCE)springer-10.1007/BF00406547 Lewis A. Department of Applied Mechanics, California Institute of Technology, 91125, Pasadena, CA, U.S.A. aut Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems [Elektronische Daten] [A. Lewis] 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. Kluwer Academic Publishers, 1992 Letters in Mathematical Physics Kluwer Academic Publishers 25/3(1992-07-01), 189-201 0377-9017 25:3<189 1992 25 11005 https://doi.org/10.1007/BF00406547 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00406547 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lewis A. Department of Applied Mechanics, California Institute of Technology, 91125, Pasadena, CA, U.S.A aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 25/3(1992-07-01), 189-201 0377-9017 25:3<189 1992 25 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer