Abstract
We construct the Runge-Lenz vector and the symmetry algebra of the rational Calogero-Coulomb problem using the Dunkl operators. We reveal that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero oscillator and oscillator models, this observation permits the claim that most of the properties of the Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of the momenta by the Dunkl momenta operators.
Original language | English |
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Article number | 022111 |
Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
Volume | 92 |
Issue number | 2 |
DOIs | |
Publication status | Published - 12 Aug 2015 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Runge-Lenz vector in the Calogero-Coulomb problem. / Hakobyan, Tigran; Nersessian, Armen.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 2, 022111, 12.08.2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Runge-Lenz vector in the Calogero-Coulomb problem
AU - Hakobyan, Tigran
AU - Nersessian, Armen
PY - 2015/8/12
Y1 - 2015/8/12
N2 - We construct the Runge-Lenz vector and the symmetry algebra of the rational Calogero-Coulomb problem using the Dunkl operators. We reveal that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero oscillator and oscillator models, this observation permits the claim that most of the properties of the Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of the momenta by the Dunkl momenta operators.
AB - We construct the Runge-Lenz vector and the symmetry algebra of the rational Calogero-Coulomb problem using the Dunkl operators. We reveal that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero oscillator and oscillator models, this observation permits the claim that most of the properties of the Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of the momenta by the Dunkl momenta operators.
UR - http://www.scopus.com/inward/record.url?scp=84939436047&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84939436047&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.92.022111
DO - 10.1103/PhysRevA.92.022111
M3 - Article
AN - SCOPUS:84939436047
VL - 92
JO - Physical Review A
JF - Physical Review A
SN - 1050-2947
IS - 2
M1 - 022111
ER -