Symplectic geometry and quantum mechanics
This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concen...
Enregistré dans:
| Auteur principal: | |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2006. |
| Collection: | Advances in Partial Differential Equations
166 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'après consultation du 27 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Symplectic geometry and quantum mechanics, advances in partial differential equations, Maurice de Gosson, Basel, Birkhäuser, 2006, 1 vol. (XX-367 p.), Operator theory, advances and applications, 3-7643-7574-4 • Symplectic Geometry and Quantum Mechanics, Texte imprimé, 9783764391256 • Symplectic geometry and quantum mechanics, advances in partial differential equations, Maurice de Gosson, Basel, Birkhäuser, 2006, 1 vol. (XX-367 p.), Operator theory, advances and applications, 3-7643-7574-4 |
| Résumé: | This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters concentrate on Lagrangian manifolds, Weyl operators and the Wigner-Moyal transform as well as on metaplectic groups and Maslov indices. Thus the keys for the mathematical description of quantum mechanics in phase space are discussed. They are followed by a rigorous geometrical treatment of the uncertainty principle. Then Hilbert-Schmidt and trace-class operators are exposed in order to treat density matrices. In the last chapter the Weyl pseudo-differential calculus is extended to phase space in order to derive a Schrödinger equation in phase space whose solutions are related to those of the usual Schrödinger equation by a wave-packet transform. The text is essentially self-contained and can be used as basis for graduate courses. Many topics are of genuine interest for pure mathematicians working in geometry and topology |
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| Description: | Description d'après consultation du 27 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. p. [355]-363. Index |
| ISBN: | 3764375752 9783764375751 |
| ISSN: | 2504-3595 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |