Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces / Edition 1

Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces / Edition 1

by Alexey V. Shchepetilov
     
 

ISBN-10: 3642071279

ISBN-13: 9783642071270

Pub. Date: 12/15/2010

Publisher: Springer Berlin Heidelberg

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

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Overview

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.

Product Details

ISBN-13:
9783642071270
Publisher:
Springer Berlin Heidelberg
Publication date:
12/15/2010
Series:
Lecture Notes in Physics Series, #707
Edition description:
Softcover reprint of hardcover 1st ed. 2006
Pages:
242
Product dimensions:
9.21(w) x 6.14(h) x 0.58(d)

Table of Contents

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.

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