Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

Alexey V. Shchepetilov (auth.)3540353844, 9783540353843, 9783540353867

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.

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Table of contents :
Two-Point Homogeneous Riemannian Spaces….Pages 1-22
Differential Operators on Smooth Manifolds….Pages 23-49
Algebras of Invariant Differential Operators on Unit Sphere Bundles Over Two-Point Homogeneous Riemannian Spaces….Pages 51-86
Hamiltonian Systems with Symmetry and Their Reduction….Pages 87-111
Two-Body Hamiltonian on Two-Point Homogeneous Spaces….Pages 113-126
Particle in a Central Field on Two-Point Homogeneous Spaces….Pages 127-160
Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces….Pages 161-190
Quasi-Exactly Solvability of the Quantum Mechanical Two-Body Problem on Spheres….Pages 191-217