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Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (Lecture Notes in Physics, 707, Band 707) - Hardcover

Shchepetilov, Alexey V.

 
9783540353843: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (Lecture Notes in Physics, 707, Band 707)
Hardcover
ISBN 10: 3540353844 ISBN 13: 9783540353843
Verlag: Springer, 2006

Inhaltsangabe

Mathematics develops both due to demands of other sciences and due to its internal logic. The latter fact explains the attention of mathematicians to many problems, which are in close connection with basic mathematical notions, even if these problems have no direct practical applications. It is well known that the space of constant curvature is one of the basic geometry notion [208], which induced the wide ?eld for investigations. As a result there were found numerous connections of constant curvature spaces with other branches of mathematics, for example, with integrable partial dif- 1 ferential equations [36, 153, 189] and with integrable Hamiltonian systems [141]. Geodesic ?ows on compact surfaces of a constant negative curvature (with the genus 2) generate many test examples for ergodic theory (see also 3 [183] and the bibliography therein). The hyperbolic space H (R) is the space of velocities in special relativity (see Sect. 7.4.1) and also arises as space-like sections in some models of general relativity.

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The present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with empahsis on spaces with constant curvature. Chapter 1-4 provide the basic notations from differential geometry for studying two-body dynamics in these spaces. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 studies the classical counterpart of the quantum system of chapter 5. Chapter 8 investigates some applications in the quantum realm, namely for the coulomb and oscillator potentials.

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Verlag
Springer
Erscheinungsdatum
2006
Sprache
Englisch
ISBN 10 
3540353844
ISBN 13 
9783540353843
Einband
Gebundene Ausgabe
Anzahl der Seiten
260
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