  We study classical and quantum dynamics on the Euclidean Taub-NUT geometry
coupled to an abelian gauge field with self-dual curvature and show that, even
though Taub-NUT has neither bounded orbits nor quantum bound states, the
magnetic binding via the gauge field produces both. The conserved Runge-Lenz
vector of Taub-NUT dynamics survives, in a modified form, in the gauged model
and allows for an essentially algebraic computation of classical trajectories
and energies of quantum bound states. We also compute scattering cross sections
and find a surprising electric-magnetic duality. Finally, we exhibit the
dynamical symmetry behind the conserved Runge-Lenz and angular momentum vectors
in terms of a twistorial formulation of phase space.
