On the classical and quantum evolution of Lagrangian half-forms in phase space

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Maurice de Gosson
Title: On the classical and quantum evolution of Lagrangian half-forms in phase space
Journal: ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE
Year: 1999
Pagination: 547-573
ISSN: 0246-0211
Publisher: GAUTHIER-VILLARS/EDITIONS ELSEVIER
City: PARIS
ISI number: 000081314300003
Organization: Blekinge Institute of Technology
Department: Department of Health, Science and Mathematics (Institutionen för hälso- och naturvetenskap)
Dept. of Health, Science and Mathematics S-371 79 Karlskrona
+46 455 38 50 00
http://www.bth.se/ihn/
Language: English
Abstract: The local expressions of a Lagrangian half-form on a quantized Lagrangian submanifold of phase space are the wavefunctions of quantum mechanics. We show that one recovers Maslov's asymptotic formula for the solutions to Schrodinger's equation if one transports these half-forms by the flow associated with a Hamiltonian H. We then consider the case when the Hamiltonian flow is replaced by the flow associated with the Bohmian, and are led to the conclusion that the use of Lagrangian half-forms leads to a quantum mechanics on phase space. (C) Elsevier, Paris.
Subject: Mathematics\Geometry
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