1.

Record Nr.

UNISA996466722903316

Autore

Shchepetilov Alexey V.

Titolo

Calculus and mechanics on two-point homogenous Riemannian spaces / / Alexey V. Shchepetilov

Pubbl/distr/stampa

Berlin, Germany : , : Springer, , [2006]

©2006

ISBN

1-280-62742-5

9786610627424

3-540-35386-0

Edizione

[1st ed. 2006.]

Descrizione fisica

1 online resource (265 p.)

Collana

Lecture Notes in Physics, , 0075-8450 ; ; 707

Disciplina

516.362

Soggetti

Riemannian manifolds

Mathematical physics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Introduction.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.