The Dirac-Coulomb problem: A mathematical revisit

A. D. Alhaidari; H. Bahlouli; M. E.H. Ismail

doi:10.1088/1751-8113/45/36/365204

The Dirac-Coulomb problem: A mathematical revisit

A. D. Alhaidari^*
, H. Bahlouli
, M. E.H. Ismail

^*Corresponding author for this work

Department of Physics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomial techniques along with the Darboux method are used to obtain the bound states energy spectrum, the relativistic scattering amplitudes and phase shifts from the asymptotic behavior of the polynomial solutions associated with the resulting three-term recursion relation.

Original language	English
Article number	365204
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	45
Issue number	36
DOIs	https://doi.org/10.1088/1751-8113/45/36/365204
State	Published - 14 Sep 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

Access to Document

10.1088/1751-8113/45/36/365204

Cite this

@article{9c13b1e9f3de49d98d4ae810c08162f7,

title = "The Dirac-Coulomb problem: A mathematical revisit",

abstract = "We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomial techniques along with the Darboux method are used to obtain the bound states energy spectrum, the relativistic scattering amplitudes and phase shifts from the asymptotic behavior of the polynomial solutions associated with the resulting three-term recursion relation.",

author = "Alhaidari, \{A. D.\} and H. Bahlouli and Ismail, \{M. E.H.\}",

year = "2012",

month = sep,

day = "14",

doi = "10.1088/1751-8113/45/36/365204",

language = "English",

volume = "45",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "36",

}

TY - JOUR

T1 - The Dirac-Coulomb problem

T2 - A mathematical revisit

AU - Alhaidari, A. D.

AU - Bahlouli, H.

AU - Ismail, M. E.H.

PY - 2012/9/14

Y1 - 2012/9/14

N2 - We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomial techniques along with the Darboux method are used to obtain the bound states energy spectrum, the relativistic scattering amplitudes and phase shifts from the asymptotic behavior of the polynomial solutions associated with the resulting three-term recursion relation.

AB - We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomial techniques along with the Darboux method are used to obtain the bound states energy spectrum, the relativistic scattering amplitudes and phase shifts from the asymptotic behavior of the polynomial solutions associated with the resulting three-term recursion relation.

UR - https://www.scopus.com/pages/publications/84865485413

U2 - 10.1088/1751-8113/45/36/365204

DO - 10.1088/1751-8113/45/36/365204

M3 - Article

AN - SCOPUS:84865485413

SN - 1751-8113

VL - 45

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 36

M1 - 365204

ER -

The Dirac-Coulomb problem: A mathematical revisit

Abstract

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this