  We solve the quantum mechanical problem of a charged particle on S^2 in the
background of a magnetic monopole for both bosonic and supersymmetric cases by
constructing Hilbert space and realizing the fundamental operators obeying
complicated Dirac bracket relations in terms of differential operators. We find
the complete energy eigenfunctions. Using the lowest energy eigenstates we
count the number of degeneracies and examine the supersymmetric structure of
the ground states in detail.
