Classical Planar Scattering by Coulombic Potentials

Softcover Nachdruck of the original 1. Auflage 1992
ISBN: 978-3-662-13900-4
Verlag: Springer

Buch, Englisch, Band 13, 142 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 276 g

Reihe: Lecture Notes in Physics Monographs

Astronomy as well as molecular physics describe non-relativistic motion by an interaction of the same form: By Newton's respectively by Coulomb's potential. But whereas the fundamental laws of motion thus have a simple form, the n-body problem withstood (for n > 2) all attempts of an explicit solution. Indeed, the studies of Poincare at the end of the last century lead to the conclusion that such an explicit solution should be impossible. Poincare himselfopened a new epoch for rational mechanics by asking qual­ itative questions like the one about the stability of the solar system. To a largeextent, his work, which was critical for the formation of differential geometry and topology, was motivated by problems arising in the analysis of the n-body problem ([38], p. 183). As it turned out, even by confining oneselfto questions ofqualitativenature, the general n-body problem could not be solved. Rather, simplified models were treated, like planar motion or the restricted 3-body problem, where the motion of a test particle did not influence the other two bodies.

Zielgruppe

Research

Autoren/Hrsg.

Knauf, Andreas

Klein, Markus

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

The Scattering Transformation.- Regularization.- Periodic Orbits.- Existence of an Invariant Cone Field.- Symbolic Dynamics.- Topological Entropy.- The Distribution of the Closed Orbits.- Fractional Dimension.- Time Delay.- Measure of the Bound States.- The Differential Cross Section.- Concluding Remarks.