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Lecture Notes in Physics

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Authors: Shchepetilov, Alexey V.

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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.

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)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • Two-Point Homogeneous Riemannian Spaces

    Pages 1-22

    Shchepetilov, Alexey V.

  • Differential Operators on Smooth Manifolds

    Pages 23-49

    Shchepetilov, Alexey V.

  • Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces

    Pages 51-86

    Shchepetilov, Alexey V.

  • Hamiltonian Systems with Symmetry and Their Reduction

    Pages 87-111

    Shchepetilov, Alexey V.

  • Two-Body Hamiltonian on Two-Point Homogeneous Spaces

    Pages 113-126

    Shchepetilov, Alexey V.

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-540-35386-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
  • ISBN 978-3-540-35384-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-07127-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces
Authors
Series Title
Lecture Notes in Physics
Series Volume
707
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-35386-7
DOI
10.1007/b11771456
Hardcover ISBN
978-3-540-35384-3
Softcover ISBN
978-3-642-07127-0
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XVIII, 242
Topics

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