H Waalkens et al 2003 J. Phys. A: Math. Gen. 36 L307 doi:10.1088/0305-4470/36/20/103
H Waalkens1,4, A Junge2,4 and H R Dullin3,4
Show affiliationsUsing 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.
03.65.Vf Phases: geometric; dynamic or topological
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
Issue 20 (23 May 2003)
Received 20 February 2003
Published 7 May 2003
H Waalkens et al 2003 J. Phys. A: Math. Gen. 36 L307
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