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)
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)