Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

  • Alexey V. Shchepetilov
Part of the Lecture Notes in Physics book series (LNP, volume 707)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Alexey V. Shchepetilov
    Pages 1-22
  3. Alexey V. Shchepetilov
    Pages 23-49
  4. Alexey V. Shchepetilov
    Pages 87-111
  5. Alexey V. Shchepetilov
    Pages 113-126
  6. Back Matter
    Pages 219-256

About this book

Introduction

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

Authors and affiliations

  • Alexey V. Shchepetilov
    • 1
  1. 1.Faculty of PhysicsM.V. Lomonosov Moscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/b11771456
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-35384-3
  • Online ISBN 978-3-540-35386-7
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361