Using modem 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.
|Translated title of the contribution||Quantum monodromy in the two-centre problem|
|Pages (from-to)||L307 - L314|
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 23 May 2003|
Bibliographical notePublisher: IOP Publishing Ltd
Other identifier: IDS number 690HA