Scattering Theory of Classical and Quantum N-Particle Systems (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
444
Utgivningsdatum
1997-06-01
Upplaga
1997 ed.
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Medarbetare
Balian, R. (red.)
Illustratör/Fotograf
15 Abb
Illustrationer
XII, 444 p.
Dimensioner
242 x 163 x 25 mm
Vikt
772 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783540620662

Scattering Theory of Classical and Quantum N-Particle Systems

av Jan Derezinski, Christian Gerard
Inbunden,  Engelska, 1997-06-01
1505
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A system of N non-relativistic classical particles interacting with pair potentials is described by a Hamiltonian of the form (0.0.1) This Hamiltonian generates a flow (t) on the phase space JR3N x JR3N. An analogous system of N quantum particles is described by a Hamiltonian of the form N 1 H := -L -Llj + L \lij(Xi - Xj)' (0.0.2) j=l 2mj l$i
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Innehållsförteckning

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 Schwartzs 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 Schurs 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 PhaseSpace 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 FIOs Associated with a Uniform Metric.- D.14 FIOs Depending on a Parameter.- References.

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