Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications / Advances in Partial Differential Equations)

Maurice A. de Gosson

ISBN 10: 3764375744 / ISBN 13: 9783764375744

Editore: Birkhauser, 2006

Riguardo questo articolo

2006 edition. 367 pages. 9.75x7.25x1.00 inches. In Stock.

Codice articolo x-3764375744

Dati bibliografici

• Titolo: Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications / Advances in Partial Differential Equations)
• Editore: Birkhauser
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 3764375744
• ISBN 13: 9783764375744
• Rilegatura: Hardcover
• Condizione: Brand New

Descrizione articolo

Riassunto

<p>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.</p>

Dalla quarta di copertina

<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>