Alexey V. Shchepetilov

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 242
• Erscheinungstermin: 4. September 2006
• Englisch
• ISBN-13: 9783540353867
• Artikelnr.: 44121018

Inhaltsangabe

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.

Rezensionen

From the reviews: "This book has eight chapters and a bibliography list containing 215 references. It is written in a clear and straightforward way that makes it useful even for nonspecialists in the field. ... In particular, the book contains interesting discussions of applications of the Poincaré section method to some problems in constant curvature spaces. ... The book is a valuable complete source for many-body problems on two-point homogeneous spaces." (Alexei Tsygvintsev, Mathematical Reviews, Issue 2008 f)