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Record Nr. |
UNISA996466722903316 |
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Autore |
Shchepetilov Alexey V. |
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Titolo |
Calculus and mechanics on two-point homogenous Riemannian spaces / / Alexey V. Shchepetilov |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer, , [2006] |
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©2006 |
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ISBN |
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1-280-62742-5 |
9786610627424 |
3-540-35386-0 |
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Edizione |
[1st ed. 2006.] |
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Descrizione fisica |
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1 online resource (265 p.) |
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Collana |
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Lecture Notes in Physics, , 0075-8450 ; ; 707 |
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Disciplina |
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Soggetti |
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Riemannian manifolds |
Mathematical physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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 |
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