05158nam 2200685Ia 450 991045426480332120200520144314.01-281-86598-297866118659861-84816-142-5(CKB)1000000000537743(EBL)1681082(OCoLC)815741824(SSID)ssj0000227421(PQKBManifestationID)11221886(PQKBTitleCode)TC0000227421(PQKBWorkID)10269841(PQKB)10267585(MiAaPQ)EBC1681082(WSP)0000P235(PPN)168237172(Au-PeEL)EBL1681082(CaPaEBR)ebr10255544(CaONFJC)MIL186598(EXLCZ)99100000000053774320010404d2001 uy 0engur|n|---|||||txtccrThe principles of Newtonian and quantum mechanics[electronic resource] the need for Planck's constant, h /M A de GossonLondon Imperial College Press ;River Edge, NJ Distributed by World Scientific Pub.c20011 online resource (382 p.)Description based upon print version of record.1-86094-274-1 Includes bibliographical references (p. [343]-351) and index.CONTENTS ; FOREWORD BY BASIL HILEY ; PREFACE ; 1 FROM KEPLER TO SCHRODINGER ... AND BEYOND ; 1.1 Classical Mechanics ; 1.2 Symplectic Mechanics ; 1.3 Action and Hamilton-Jacobi's Theory ; 1.4 Quantum Mechanics ; 1.5 The Statistical Interpretation of w1.6 Quantum Mechanics in Phase Space 1.7 Feynman's ""Path Integral"" ; 1.8 Bohmian Mechanics ; 1.9 Interpretations ; 2 NEWTONIAN MECHANICS ; 2.1 Maxwell's Principle and the Lagrange Form ; 2.2 Hamilton's Equations ; 2.3 Galilean Covariance2.4 Constants of the Motion and Integrable Systems 2.5 Liouville's Equation and Statistical Mechanics ; 3 THE SYMPLECTIC GROUP ; 3.1 Symplectic Matrices and Sp(n) ; 3.2 Symplectic Invariance of Hamiitonian Flows ; 3.3 The Properties of Sp(n) ; 3.4 Quadratic Hamiltonians3.5 The Inhomogeneous Symplectic Group 3.6 An Illuminating Analogy ; 3.7 Gromov's Non-Squeezing Theorem ; 3.8 Symplectic Capacity and Periodic Orbits ; 3.9 Capacity and Periodic Orbits ; 3.10 Cell Quantization of Phase Space ; 4 ACTION AND PHASE ; 4.1 Introduction4.2 The Fundamental Property of the Poincare-Cartan Form 4.3 Free Symplectomorphisms and Generating Functions ; 4.4 Generating Functions and Action ; 4.5 Short-Time Approximations to the Action ; 4.6 Lagrangian Manifolds ; 4.7 The Phase of a Lagrangian Manifold4.8 Keller-Maslov Quantization This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introducLagrangian functionsMaslov indexGeometric quantizationElectronic books.Lagrangian functions.Maslov index.Geometric quantization.530.12Gosson Maurice de67588MiAaPQMiAaPQMiAaPQBOOK9910454264803321The principles of Newtonian and quantum mechanics2151681UNINA