Scattering Theory of Classical and Quantum N-Particle Systems
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Scattering Theory of Classical and Quantum N-Particle Systems: (Theoretical and Mathematical Physics)

Scattering Theory of Classical and Quantum N-Particle Systems: (Theoretical and Mathematical Physics)


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About the Book

This monograph presents time-dependant methods for studying problems of scattering theory in classical and quantum mechanics. Particualar attention is paid to long-range potentials. For a large class of interactions, the existence of the asymptotic velocity and the asymtotic velocity and the asymtotic completeness of the wave operators is shown. The text explains the analogy between classical and quantum scattering theory.

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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Product Details
  • ISBN-13: 9783540620662
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 234 mm
  • No of Pages: 444
  • Returnable: Y
  • Width: 156 mm
  • ISBN-10: 3540620664
  • Publisher Date: 05 Jun 1997
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: Theoretical and Mathematical Physics


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