Scattering theory of classical and quantum N-particle systems

書誌事項

Scattering theory of classical and quantum N-particle systems

Jan Dereziński, Christian Gérard

(Texts and monographs in physics)

Springer, [2011?]

Softcover reprint of the hardcover 1st edition 1977

  • pbk.

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注記

Originally published: 1997

Includes bibliographical references and index

内容説明・目次

内容説明

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

目次

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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詳細情報

  • NII書誌ID(NCID)
    BB1256007X
  • ISBN
    • 9783642082849
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin
  • ページ数/冊数
    xii, 444p.
  • 大きさ
    24 cm
  • 親書誌ID
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