Calculus and mechanics on two-point homogenous Riemannian spaces
- Alexey V. Shchepetilov.
- Berlin : Springer, 2006.
- Physical description
- xvii, 255 p. : ill. ; 25 cm.
- Lecture notes in physics 707.
- Shchepetilov, Alexey V.
- Includes bibliographical references and index.
- Two-Point Homogeneous Riemannian Spaces.- Differential Operators on Smooth Manifolds.- Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Tow-Point Homogeneous Riemannian Spaces.- Hamiltonian Systems With Symmetry And Their Reduction.- Tow-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.- Calculations of Commutator Relations for Algebras of Invariant Differential Operator.- Some Fuchsian Differential Equations.- Orthogonal Complex Lie Algebras and Their Representations.- Unsolved Problems.
- (source: Nielsen Book Data)
- Publisher's Summary
- The present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with emphasis 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.
(source: Nielsen Book Data)
- Publication date
- Lecture notes in physics, 0075-8450 ; 707
- Also available on the World Wide Web.
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