03079nam 2200637 450 991014662780332120220915113837.01-280-62742-597866106274243-540-35386-010.1007/b11771456(CKB)1000000000282256(EBL)3036491(SSID)ssj0000116789(PQKBManifestationID)11898342(PQKBTitleCode)TC0000116789(PQKBWorkID)10036223(PQKB)11296544(DE-He213)978-3-540-35386-7(MiAaPQ)EBC3036491(MiAaPQ)EBC6872096(Au-PeEL)EBL6872096(PPN)258845643(PPN)123136016(EXLCZ)99100000000028225620220915d2006 uy 0engur|n|---|||||txtccrCalculus and mechanics on two-point homogenous Riemannian spaces /Alexey V. Shchepetilov1st ed. 2006.Berlin, Germany :Springer,[2006]©20061 online resource (265 p.)Lecture Notes in Physics,0075-8450 ;707Introduction.3-540-35384-4 Includes bibliographical references and index.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.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.Lecture Notes in Physics,0075-8450 ;707Riemannian manifoldsMathematical physicsRiemannian manifolds.Mathematical physics.516.362Shchepetilov Alexey V.501717MiAaPQMiAaPQMiAaPQBOOK9910146627803321Calculus and mechanics on two-point homogenous riemannian spaces727284UNINA