Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

• Main Author: Shchepetilov, Alexey V. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Physics, 707
• Subjects: Physics.; Differential geometry.; Mechanics.; Mathematical Methods in Physics.; Differential Geometry.

 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. 

 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.