Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces

2006
ISBN: 978-3-540-35384-3
Verlag: Springer

Buch, Englisch, 242 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1250 g

Reihe: Lecture Notes in Physics

This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. 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 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.

Zielgruppe

Research

Autoren/Hrsg.

Shchepetilov, Alexey V.

Fachgebiete

• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik

Inhaltsverzeichnis

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.