Symplectic Geometry and Quantum Mechanics: 166 (Operator Theory: Advances and Applications) - Hardcover

De Gosson, Maurice A.

Hardcover

ISBN 10: 3764375744 ISBN 13: 9783764375744

Verlag: Birkhäuser, 2006

Inhaltsangabe

This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

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<p>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&nbsp; rigorous presentation of the basics of symplectic geometry and of its multiply-oriented extension. Further chapters&nbsp;concentrate on&nbsp;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&nbsp;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.</p><p>The text is essentially self-contained and can be used as basis for graduate courses. Many topics are&nbsp;of genuine interest for pure mathematicians working in geometry and topology.</p>

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2006
• Sprache: Englisch
• ISBN 10: 3764375744
• ISBN 13: 9783764375744
• Einband: Tapa dura
• Anzahl der Seiten: 392
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar