SYMMETRIES AND DEGENERACIES OF A CHARGED OSCILLATOR IN THE FIELD OF A MAGNETIC MONOPOLE

The constants of motion responsible for the level degeneracy of a charged, spin 0 particle subjected to harmonic and centrifugal forces and to the field of a magnetic monopole are obtained. Operators closing onto the SU(2) +SU(2) algebra are constructed in terms of these conserved quantities. The space of states decomposes into SU(2) + SU(2) irreducible modules whose dimensions coincide with the degree of degeneracy of the various energy levels.