LEADER 03077nam 2200637 450 001 996466722903316 005 20220915113837.0 010 $a1-280-62742-5 010 $a9786610627424 010 $a3-540-35386-0 024 7 $a10.1007/b11771456 035 $a(CKB)1000000000282256 035 $a(EBL)3036491 035 $a(SSID)ssj0000116789 035 $a(PQKBManifestationID)11898342 035 $a(PQKBTitleCode)TC0000116789 035 $a(PQKBWorkID)10036223 035 $a(PQKB)11296544 035 $a(DE-He213)978-3-540-35386-7 035 $a(MiAaPQ)EBC3036491 035 $a(MiAaPQ)EBC6872096 035 $a(Au-PeEL)EBL6872096 035 $z(PPN)258845643 035 $a(PPN)123136016 035 $a(EXLCZ)991000000000282256 100 $a20220915d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCalculus and mechanics on two-point homogenous Riemannian spaces /$fAlexey V. Shchepetilov 205 $a1st ed. 2006. 210 1$aBerlin, Germany :$cSpringer,$d[2006] 210 4$dİ2006 215 $a1 online resource (265 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v707 300 $aIntroduction. 311 $a3-540-35384-4 320 $aIncludes bibliographical references and index. 327 $aTwo-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. 330 $aThe present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with empahsis on spaces with constant curvature. Chapter 1-4 provide the basic notations from differential geometry for studying two-body dynamics in these spaces. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 studies the classical counterpart of the quantum system of chapter 5. Chapter 8 investigates some applications in the quantum realm, namely for the coulomb and oscillator potentials. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v707 606 $aRiemannian manifolds 606 $aMathematical physics 615 0$aRiemannian manifolds. 615 0$aMathematical physics. 676 $a516.362 700 $aShchepetilov$b Alexey V.$0501717 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466722903316 996 $aCalculus and mechanics on two-point homogenous riemannian spaces$9727284 997 $aUNISA