Overview

This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in classical and quantum mechanics. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. A special feature is its emphasis to show the beautiful analogy between classical and quantum scattering theory.

Full Product Details

Author:   Jan Derezinski ,  Christian Gerard
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1997
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.700kg
ISBN:  

9783642082849

ISBN 10:   364208284
Pages:   444
Publication Date:   07 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

0. Introduction.- 1. Classical Time-Decaying Forces.- 2. Classical 2-Body Hamiltonians.- 3. Quantum Time-Decaying Hamiltonians.- 4. Quantum 2-Body Hamiltonians.- 5. Classical N-Body Hamiltonians.- 6. Quantum N-Body Hamiltonians.- A. Miscellaneous Results in Real Analysis.- A.1 Some Inequalities.- A.2 The Fixed Point Theorem.- A.3 The Hamilton-Jacobi Equation.- A.4 Construction of Some Cutoff Functions.- A.5 Propagation Estimates.- A.6 Comparison of Two Dynamics.- A.7 Schwartz’s Global Inversion Theorem.- B. Operators on Hilbert Spaces.- B.1 Self-adjoint Operators.- B.2 Convergence of Self-adjoint Operators.- B.3 Time-Dependent Hamiltonians.- B.4 Propagation Estimates.- B.5 Limits of Unitary Operators.- B.6 Schur’s Lemma.- C. Estimates on Functions of Operators.- C.1 Basic Estimates of Commutators.- C.2 Almost-Analytic Extensions.- C.3 Commutator Expansions I.- C.4 Commutator Expansions II.- D. Pseudo-differential and Fourier Integral Operators.- D.0 Introduction.- D.1 Symbols of Operators.- D.2 Phase—Space Correlation Functions.- D.3 Symbols Associated with a Uniform Metric.- D.4 Pseudo-differential Operators Associated with a Uniform Metric.- D.5 Symbols and Operators Depending on a Parameter.- D.6 Weighted Spaces.- D.7 Symbols Associated with Some Non-uniform Metrics.- D.8 Pseudo-differential Operators Associated with the Metric 91.- D.9 Essential Support of Pseudo-differential Operators.- D.10 Ellipticity.- D.12 Non-stationary Phase Method.- D.13 FIO’s Associated with a Uniform Metric.- D.14 FIO’s Depending on a Parameter.- References.

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