On the notion of phase in mechanics
| Document type: | Journal Articles |
|---|---|
| Article type: | Original article |
| Peer reviewed: | Yes |
| Author(s): | Maurice de Gosson |
| Title: | On the notion of phase in mechanics |
| Journal: | JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL |
| Year: | 2004 |
| Pagination: | 7297-7314 |
| ISSN: | 0305-4470 |
| Publisher: | IOP PUBLISHING LTD |
| City: | BRISTOL |
| URI/DOI: | 10.1088/0305-4407/37/29/008 |
| ISI number: | 000223254200012 |
| 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 notion of phase plays an essential role in both semiclassical and quantum mechanics. But what is exactly a phase, and how does it change with time? It turns out that the most universal definition of a phase can be given in terms of Lagrangian manifolds by exploiting the properties of the Poincare-Cartan form. Such a phase is defined, not in configuration space, but rather in phase-space and is thus insensitive to the appearance of caustics. Surprisingly enough, this approach allows us to recover the Heisenberg-Weyl formalism without invoking commutation relations for observables. |
| Subject: | Mathematics\Geometry |
