Quantum monodromy in the two-centre problem

Using modern tools from the geometric theory of Hamiltonian systems it is shown that electronic excitations in diatoms which can be modelled by the two-centre problem exhibit a complicated case of classical and quantum monodromy. This means that there is an obstruction to the existence of global quantum numbers in these classically integrable systems. The symmetric case of H+2 and the asymmetric case of H He++ are explicitly worked out. The asymmetric case has a non-local singularity causing monodromy. It coexists with a second singularity which is also present in the symmetric case. An interpretation of monodromy is given in terms of the caustics of invariant tori.