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  • © 2006

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Part of the book series: Lecture Notes in Physics (LNP, volume 707)

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  • ISBN: 978-3-540-35386-7
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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XVII
  2. Two-Point Homogeneous Riemannian Spaces

    • Alexey V. Shchepetilov
    Pages 1-22
  3. Differential Operators on Smooth Manifolds

    • Alexey V. Shchepetilov
    Pages 23-49
  4. Hamiltonian Systems with Symmetry and Their Reduction

    • Alexey V. Shchepetilov
    Pages 87-111
  5. Two-Body Hamiltonian on Two-Point Homogeneous Spaces

    • Alexey V. Shchepetilov
    Pages 113-126
  6. Back Matter

    Pages 219-256

About this book

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.

Keywords

  • Hamiltonian functions
  • Potential
  • Riemannian spaces
  • curvature
  • differential geometry
  • integrable systems
  • manifold
  • two-body problem

Reviews

From the reviews:

"This book has eight chapters and a bibliography list containing 215 references. It is written in a clear and straightforward way that makes it useful even for nonspecialists in the field. … In particular, the book contains interesting discussions of applications of the Poincaré section method to some problems in constant curvature spaces. … The book is a valuable complete source for many-body problems on two-point homogeneous spaces." (Alexei Tsygvintsev, Mathematical Reviews, Issue 2008 f)

Authors and Affiliations

  • Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia

    Alexey V. Shchepetilov

Bibliographic Information

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-35386-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 109.00
Price excludes VAT (USA)