  We study gauged Laplacian operators on line bundles on a quantum
2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows
for their complete diagonalization. These operators describe `excitations
moving on the quantum sphere' in the field of a magnetic monopole. The energies
are not invariant under the exchange monopole/antimonopole, that is under
inverting the direction of the magnetic field. There are potential applications
to models of quantum Hall effect.
