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DTSTART:20151025T010000
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DTSTART;TZID=Europe/Rome:20150603T143000
DTEND;TZID=Europe/Rome:20150603T160000
DTSTAMP:20260512T162549
CREATED:20171026T122350Z
LAST-MODIFIED:20171026T122350Z
UID:6895-1433341800-1433347200@w3.lnf.infn.it
SUMMARY:Runge-Lenz vector and Stark effect in  Calogero-Coulomb problem
DESCRIPTION:We show that deformation N-dimensional (Euclidean\, spherical and hyperbolic) Coulomb system by the patential of rational Calogero model preserves superintegrability property of Coulomb problem. Then we find explicit expression of the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem\, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterparts. This observation permits to claim that most of properties of Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of momenta by Dunkl momenta operators. Particularly \, we show that N-dimensional Calogero-Coulomb system preserves integrability property in the presence of Stark term\, and construct its complete set of constants of motion. We find\, that in parabolic coordinates the systems admits complete separation of variables for N=2\,3 and partial ones for $N>3$. The system possesses linear Stark effect and find its explicit expression.Finally\, we show\, that two-center Calodjero-Coulomb problem is also integrable systems\, which admits\, in elliptic coordinates\, the complet separation of variables for N=2\,3 and partial ones for N>3.
URL:/event/runge-lenz-vector-and-stark-effect-in-calogero-coulomb-problem/
LOCATION:Aula Seminari\, Via Enrico Fermi\, 40\, Frascati\, Roma\, 00044\, Italia
CATEGORIES:Seminari teorici
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