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 |
