Shchepetilov, Alexey V. <br/><br/>
Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces  [electronic resource] / 
by Alexey V. Shchepetilov. 
 - XVIII, 242 p.  online resource. 
 - Lecture Notes in Physics,  707  0075-8450 ; .
 - Lecture Notes in Physics,  707 .
<br/><br/>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. 
<br/><br/>ZDB-2-PHA ZDB-2-LNP 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9783540353867 
<br/><br/><label>Standard No.: </label>10.1007/b11771456  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Physics.<br/>Global differential geometry.<br/>Mathematical physics.<br/>Mechanics.<br/>Physics.<br/>Mathematical Methods in Physics.<br/>Differential Geometry.<br/>Mechanics.
<br/><br/><label>LC Class. No.: </label>QC5.53 
<br/><br/><label>Dewey Class. No.: </label>530.15