  We derive the single-particle eigenenergies and eigenfunctions for massless
Dirac fermions confined to the surface of a sphere in the presence of a
magnetic monopole, i.e., we solve the Landau level problem for electrons in
graphene on the Haldane sphere. With the single-particle eigenfunctions and
eigenenergies we calculate the Haldane pseudopotentials for the Coulomb
interaction in the second Landau level and calculate the effective
pseudopotentials characterizing an effective Landau level mixing Hamiltonian
entirely in the spherical geometry to be used in theoretical studies of the
fractional quantum Hall effect in graphene. Our treatment is analogous to the
formalism in the planar geometry and reduces to the planar results in the
thermodynamic limit.
