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Scattering Theory of Classical and Quantum N-Particle Systems - Jan Derezinski, Christian Gerard

Scattering Theory of Classical and Quantum N-Particle Systems

Buch | Softcover
XII, 444 Seiten
2010 | 1. Softcover reprint of hardcover 1st ed. 1997
Springer Berlin (Verlag)
978-3-642-08284-9 (ISBN)
CHF 149,75 inkl. MwSt
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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 Ct. (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

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.

Erscheint lt. Verlag 7.12.2010
Reihe/Serie Theoretical and Mathematical Physics
Zusatzinfo XII, 444 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 684 g
Themenwelt Naturwissenschaften Physik / Astronomie Astronomie / Astrophysik
Naturwissenschaften Physik / Astronomie Hochenergiephysik / Teilchenphysik
Naturwissenschaften Physik / Astronomie Quantenphysik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Mechanics • Potential • quantum mechanics • scattering theory
ISBN-10 3-642-08284-X / 364208284X
ISBN-13 978-3-642-08284-9 / 9783642082849
Zustand Neuware
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