Calculus and mechanics on two-point homogenous riemannian spaces
- Author
- Alexey V. Shchepetilov
- Publication Year
- 2006
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Physics
- Download Book Read book
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.
Keywords: Physics and Astronomy / Hamiltonian functions / Potential / Riemannian spaces / Curvature / Differential geometry / Integrable systems / Manifold / Two-body problem
