An algebraic treatment of the MIC-Kepler problem on S³ sphere

The quantum-mechanical problem of motion in a dual charged Coulomb field modified by a centrifugal term (MIC-Kepler problem) is considered in a three-dimensional space of constant positive curvature, S-3. Conserved operators are found, and their commutation relations are derived. It is shown that, in the MIC-Kepler problem in S-3 space, conserved operators form a cubic algebra similar to that of the Kepler problem in the same space. This symmetry algebra is used to obtain the energy spectrum of the problem. (C) 2002 MAIK "Nauka/Interperiodica".