  The appearance of noncommuting spatial coordinates is studied in quantum
systems containing a magnetic monopole and under the influence of a radial
potential. We derive expressions for the commutators of the coordinates that
have been restricted to the lowest energy level. Quantum corrections are found
to previous results by Frenkel and Pereira based on quantizing the Dirac
brackets of the classical theory. For two different potentials, the modified
harmonic oscillator potential and the modified Coulomb potential, we also
calculate the commutators for a projection to a fixed energy level.
