Runge-Lenz vector in the Calogero-Coulomb problem

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
Article number	022111
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	92
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.92.022111
Publication status	Published - 12 Aug 2015

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

Access to Document

10.1103/PhysRevA.92.022111

Fingerprint Dive into the research topics of 'Runge-Lenz vector in the Calogero-Coulomb problem'. Together they form a unique fingerprint.

Cite this

@article{7db6d1207d4d4533b777082a5d67eeac,

title = "Runge-Lenz vector in the Calogero-Coulomb problem",

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.",

author = "Tigran Hakobyan and Armen Nersessian",

year = "2015",

month = aug,

day = "12",

doi = "10.1103/PhysRevA.92.022111",

language = "English",

volume = "92",

journal = "Physical Review A",

issn = "1050-2947",

publisher = "American Physical Society",

number = "2",

}

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 -