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Symplectic Geometry And Quantum Mechanics, Hardcover by Gosson, Maurice De, B...
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- Book Title
- Symplectic Geometry And Quantum Mechanics
- ISBN
- 9783764375744
- Subject Area
- Science, Mathematics
- Publication Name
- Symplectic Geometry and Quantum Mechanics
- Publisher
- Springer Basel A&G
- Item Length
- 9.3 in
- Subject
- Group Theory, Topology, Differential Equations / Partial, Physics / Mathematical & Computational
- Publication Year
- 2006
- Series
- Operator Theory: Advances and Applications Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Weight
- 74.8 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xx, 368 Pages
關於產品
Product Information
Introduction We have been experiencing since the 1970s a process of "symplectization" of S- ence especially since it has been realized that symplectic geometry is the natural language of both classical mechanics in its Hamiltonian formulation, and of its re'nement,quantum mechanics. The purposeof this bookis to providecorema- rial in the symplectic treatment of quantum mechanics, in both its semi-classical and in its "full-blown" operator-theoretical formulation, with a special emphasis on so-called phase-space techniques. It is also intended to be a work of reference for the reading of more advanced texts in the rapidly expanding areas of sympl- tic geometry and topology, where the prerequisites are too often assumed to be "well-known"bythe reader. Thisbookwillthereforebeusefulforbothpurema- ematicians and mathematical physicists. My dearest wish is that the somewhat novel presentation of some well-established topics (for example the uncertainty principle and Schrod ¨ inger's equation) will perhaps shed some new light on the fascinating subject of quantization and may open new perspectives for future - terdisciplinary research. I have tried to present a balanced account of topics playing a central role in the "symplectization of quantum mechanics" but of course this book in great part represents my own tastes. Some important topics are lacking (or are only alluded to): for instance Kirillov theory, coadjoint orbits, or spectral theory. We will moreover almost exclusively be working in ?at symplectic space: the slight loss in generality is, from my point of view, compensated by the fact that simple things are not hidden behind complicated "intrinsic" notation.
Product Identifiers
Publisher
Springer Basel A&G
ISBN-10
3764375744
ISBN-13
9783764375744
eBay Product ID (ePID)
51822778
Product Key Features
Number of Pages
Xx, 368 Pages
Language
English
Publication Name
Symplectic Geometry and Quantum Mechanics
Publication Year
2006
Subject
Group Theory, Topology, Differential Equations / Partial, Physics / Mathematical & Computational
Type
Textbook
Subject Area
Science, Mathematics
Series
Operator Theory: Advances and Applications Ser.
Format
Hardcover
Dimensions
Item Weight
74.8 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2017-400563
Dewey Edition
22
Reviews
From the reviews: "De Gosson's book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Cr'smareanu, Analele Stiintifice "This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. ... This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. ... the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e) "This book covers ... symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. ... The exposition is very detailed and complete proofs are given. ... the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques." (R. Steinbauer, Monatshefte für Mathematik, Vol. 155 (1), September, 2008), From the reviews: "De Gosson's book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Crsmareanu, Analele Stiintifice "This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. ... This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. ... the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e) "This book covers ... symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. ... The exposition is very detailed and complete proofs are given. ... the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques." (R. Steinbauer, Monatshefte fr Mathematik, Vol. 155 (1), September, 2008), From the reviews:"De Gosson's book is an exhaustive and clear description of almost all the more recent results obtained in connected areas of research like symplectiv geometry, the combinatorial theory of the Maslov index, the theory of the metaplectic group and so on. It fills an important niche in the literature." -Mircea Cr'smareanu, Analele Stiintifice"This book concerns certain aspects of symplectic geometry and their application to quantum mechanics. … This book seems best suited to someone who already has a solid background in quantum theory and wants to learn more about the symplectic geometric techniques used in quantization. … the book contains useful information about various important topics." (Brian C. Hall, Mathematical Reviews, Issue 2007 e)This book covers … symplectic geometry and their applications in quantum mechanics with an emphasis on phase space methods. … The exposition is very detailed and complete proofs are given. … the book takes a particularly fresh point of view on some of the topics and contains a lot of useful information for readers with some background in quantum theory and an interest in the use of symplectic techniques. (R. Steinbauer, Monatshefte für Mathematik, Vol. 155 (1), September, 2008)
Series Volume Number
166
Number of Volumes
1 Vol.
Illustrated
Yes
Dewey Decimal
516.3/62
Lc Classification Number
Qa252.3
Table of Content
Symplectic Geometry.- Symplectic Spaces and Lagrangian Planes.- The Symplectic Group.- Multi-Oriented Symplectic Geometry.- Intersection Indices in Lag(n) and Sp(n).- Heisenberg Group, Weyl Calculus, and Metaplectic Representation.- Lagrangian Manifolds and Quantization.- Heisenberg Group and Weyl Operators.- The Metaplectic Group.- Quantum Mechanics in Phase Space.- The Uncertainty Principle.- The Density Operator.- A Phase Space Weyl Calculus.
Copyright Date
2006
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