Dynamical symmetries in a spherical geometry. I
Abstract
Some aspects of classical and quantum particle mechanics on a sphere are investigated. It is shown that in a certain coordinate system, which is associated with a certain projection of the Nsphere onto a tangent Nplane, closed orbits occur for the same potentials as in Euclidean geometry. Corresponding vector or tensor constants of motion and their Poisson bracket algebras are constructed, as are the corresponding quantum mechanical operators and commutator algebras. The Hamiltonians of the quantum mechanical Kepler and isotropic oscillator systems on a 2sphere are expressed as functions of the Casimir operators of the groups SO(3) and SU(2), respectively. It is shown how the generators of the dynamical symmetries of these systems can be used, in a Schroedinger representation, to construct wavefunctions.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 1979
 DOI:
 10.1088/03054470/12/3/006
 Bibcode:
 1979JPhA...12..309H
 Keywords:

 Euclidean Geometry;
 Nonrelativistic Mechanics;
 Particle Motion;
 Angular Momentum;
 Classical Mechanics;
 Dynamic Characteristics;
 Eigenvectors;
 Energy Levels;
 Hamiltonian Functions;
 Lie Groups;
 Poisson Equation;
 Quantum Mechanics;
 Symmetry;
 Physics (General)