Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction

Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2017) Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction. Annals of Physics, 380 121-134. doi:10.1016/j.aop.2017.03.003


Author Hoque, Md Fazlul
Marquette, Ian
Zhang, Yao-Zhong
Title Quadratic algebra structure in the 5D Kepler system with non-central potentials and Yang–Coulomb monopole interaction
Journal name Annals of Physics   Check publisher's open access policy
ISSN 1096-035X
0003-4916
Publication date 2017-05-01
Sub-type Article (original research)
DOI 10.1016/j.aop.2017.03.003
Open Access Status Not yet assessed
Volume 380
Start page 121
End page 134
Total pages 14
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Collection year 2018
Language eng
Formatted abstract
We construct the integrals of motion for the 5D deformed Kepler system with non-central potentials in su(2) Yang–Coulomb monopole field. We show that these integrals form a higher rank quadratic algebra Q(3;Lso(4),Tsu(2))⊕so(4), with structure constants involving the Casimir operators of so(4) and su(2) Lie algebras. We realize the quadratic algebra in terms of the deformed oscillator and construct its finite-dimensional unitary representations. This enable us to derive the energy spectrum of the system algebraically. Furthermore we show that the model is multiseparable and allows separation of variables in the hyperspherical and parabolic coordinates. We also show the separability of its 8D dual system (i.e. the 8D singular harmonic oscillator) in the Euler and cylindrical coordinates.
Keyword Monopole interaction
Orthogonal polynomials
Oscillator algebras
Quadratic algebras
Schrödinger equation
Superintegrable
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
HERDC Pre-Audit
 
Versions
Version Filter Type
Citation counts: Scopus Citation Count Cited 0 times in Scopus Article
Google Scholar Search Google Scholar
Created: Tue, 11 Apr 2017, 00:25:16 EST by Web Cron on behalf of Learning and Research Services (UQ Library)