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Classical N-Body Hamiltonians

  • Jan Dereziński
  • Christian Gérard
Chapter
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

A system of N non-relativistic particles moving in Euclidean space ℝ v is described with phase space ℝ Nv × ℝ Nv , with the coordinates
$$(x{}_1,...,{x_N},{\xi _1},...,{\xi _N})$$
, where (x i , ξ i ) are the position and momentum of the i-th particle. Its motion is described by the Hamiltonian
$$H(x,\xi ) = \sum\limits_{i = 1}^N {\frac{{\xi _i^2}}{{2{m_i}}}} + \sum\limits_{i < j} {{V_{ij}}} V({x_i} - {x_j})$$
(5.0.1)
, where m i is the mass of the i-th particle and V ij(x) is the interaction potential between particles i and j. The most important case of such a Hamiltonian is the one encountered in celestial mechanics where11111Typical assumptions that we will keep in mind in this chapter are
$${V_{ij}}(x) = \frac{{ - {m_i}{m_j}}}{{\left| x \right|}}$$
(5.0.2)
.

Keywords

Configuration Space Quantum Case Free Region Asymptotic Completeness Trapping Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jan Dereziński
    • 1
  • Christian Gérard
    • 2
  1. 1.Department of Mathematical Methods in PhysicsWarsaw UniversityWarsawPoland
  2. 2.Centre de MathématiquesEcole PolytechniquePalaiseau CedexFrance

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