Higgs Algebraic Symmetry of Screened System in a Spherical Geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wu and J.Y. Zeng, Phys. Rev. A 62 (2000) 032509], We find similar properties in the corresponding systems in a spherical space, whose dynamical symmet...

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Published inCommunications in theoretical physics Vol. 60; no. 3; pp. 278 - 282
Main Authors Li, Yan, Zhang, Fu-Lin, Gu, Rui-Juan, Chen, Jing-Ling
Format Journal Article
LanguageEnglish
Published 01.09.2013
Subjects
Algebra
Angular momentum
Coulomb potential
Dynamical systems
Dynamics
Mathematical analysis
Orbits
Symmetry
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Summary:The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wu and J.Y. Zeng, Phys. Rev. A 62 (2000) 032509], We find similar properties in the corresponding systems in a spherical space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of closed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.
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content type line 23
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/60/3/04