Monodromy, diabolic points, and angular momentum coupling

Monodromy, or the most basic obstruction to global action-angle coordinates is shown to be present in the well known problem of two coupled angular mo menta. It is also shown that in the corresponding quantum problem monodromy manifests itself as the redistribution of energy levels between different multiplets of the quantum spectrum. (C) 1999 Elsevier Science B.V. All righ ts reserved.