Quasi-exactly solvable relativistic soft-core Coulomb models

Agboola, Davids and Zhang, Yao-Zhong (2012) Quasi-exactly solvable relativistic soft-core Coulomb models. Annals of Physics, 327 9: 2275-2287. doi:10.1016/j.aop.2012.07.002

Author Agboola, Davids
Zhang, Yao-Zhong
Title Quasi-exactly solvable relativistic soft-core Coulomb models
Journal name Annals of Physics   Check publisher's open access policy
ISSN 0003-4916
Publication date 2012-09
Sub-type Article (original research)
DOI 10.1016/j.aop.2012.07.002
Volume 327
Issue 9
Start page 2275
End page 2287
Total pages 13
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Collection year 2013
Language eng
Formatted abstract
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein–Gordon and Dirac equations with the family of soft-core Coulomb potentials Vq(r)=−Z/(rq+βq)1/q, Z>0, β>0, q≥1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations.
Keyword Soft-core potential
Bethe ansatz method
Quasi-exactly solvable system
Dirac equation
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
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Citation counts: TR Web of Science Citation Count  Cited 4 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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