Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces / Edition 1

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This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. 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 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.

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Editorial Reviews

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"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)

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Product Details

  • ISBN-13: 9783642071270
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/15/2010
  • Series: Lecture Notes in Physics Series, #707
  • Edition description: Softcover reprint of hardcover 1st ed. 2006
  • Edition number: 1
  • Pages: 242
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.58 (d)

Table of Contents

Two-Point Homogeneous Riemannian Spaces.- Differential Operators on Smooth Manifolds.- Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces.- Hamiltonian Systems with Symmetry and Their Reduction.- Two-Body Hamiltonian on Two-Point Homogeneous Spaces.- Particle in a Central Field on Two-Point Homogeneous Spaces.- Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces.- Quasi-Exactly Solvability of the Quantum Mechanical Two-Body Problem on Spheres.

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