Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations

I. A. Assi; H. Bahlouli; A. D. Alhaidari

doi:10.1063/1.4953124

Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations

I. A. Assi^*, H. Bahlouli, A. D. Alhaidari

^*Corresponding author for this work

Department of Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

The aim of this research is to extend the class of solvable potentials of Dirac equation as a continuation to the work in [1]. We expand the spinor wavefunction in a square integrable spinor basis functions in which the expansion coefficients are functions of energy and potential parameters. Requiring the wave operator, J = H - E, to be tridiagonal and symmetric, this transforms the wave equation to a three-term recursion relation for the expansion coefficients which can be solved using known mathematical results on orthogonal polynomials. For illustration, we restricted ourselves here to the so-called Laguerre basis and considered situations where the obtained recursion relations can be easily compared to the ones associated with a well-known class of orthogonal polynomials.

Original language	English
Title of host publication	Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016
Editors	Abdelrahman Mahdy, Nurdogan Can, Ali Al-Kamli, Mohamed Fadhali, Galib Omar Souadi, Mahmoud Mahgoub
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413993
DOIs	https://doi.org/10.1063/1.4953124
State	Published - 10 Jun 2016

Publication series

Name	AIP Conference Proceedings
Volume	1742
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Bibliographical note

Publisher Copyright:
© 2016 Author(s).

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.4953124

Cite this

Assi, I. A., Bahlouli, H., & Alhaidari, A. D. (2016). Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations. In A. Mahdy, N. Can, A. Al-Kamli, M. Fadhali, G. O. Souadi, & M. Mahgoub (Eds.), Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016 Article 030003 (AIP Conference Proceedings; Vol. 1742). American Institute of Physics Inc.. https://doi.org/10.1063/1.4953124

Assi, I. A. ; Bahlouli, H. ; Alhaidari, A. D. / Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations. Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016. editor / Abdelrahman Mahdy ; Nurdogan Can ; Ali Al-Kamli ; Mohamed Fadhali ; Galib Omar Souadi ; Mahmoud Mahgoub. American Institute of Physics Inc., 2016. (AIP Conference Proceedings).

@inproceedings{cff5293a55514ce592c3f8953786fcfc,

title = "Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations",

abstract = "The aim of this research is to extend the class of solvable potentials of Dirac equation as a continuation to the work in [1]. We expand the spinor wavefunction in a square integrable spinor basis functions in which the expansion coefficients are functions of energy and potential parameters. Requiring the wave operator, J = H - E, to be tridiagonal and symmetric, this transforms the wave equation to a three-term recursion relation for the expansion coefficients which can be solved using known mathematical results on orthogonal polynomials. For illustration, we restricted ourselves here to the so-called Laguerre basis and considered situations where the obtained recursion relations can be easily compared to the ones associated with a well-known class of orthogonal polynomials.",

author = "Assi, \{I. A.\} and H. Bahlouli and Alhaidari, \{A. D.\}",

note = "Publisher Copyright: {\textcopyright} 2016 Author(s).",

year = "2016",

month = jun,

day = "10",

doi = "10.1063/1.4953124",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Abdelrahman Mahdy and Nurdogan Can and Ali Al-Kamli and Mohamed Fadhali and Souadi, \{Galib Omar\} and Mahmoud Mahgoub",

booktitle = "Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016",

}

Assi, IA, Bahlouli, H & Alhaidari, AD 2016, Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations. in A Mahdy, N Can, A Al-Kamli, M Fadhali, GO Souadi & M Mahgoub (eds), Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016., 030003, AIP Conference Proceedings, vol. 1742, American Institute of Physics Inc. https://doi.org/10.1063/1.4953124

Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations. / Assi, I. A.; Bahlouli, H.; Alhaidari, A. D.
Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016. ed. / Abdelrahman Mahdy; Nurdogan Can; Ali Al-Kamli; Mohamed Fadhali; Galib Omar Souadi; Mahmoud Mahgoub. American Institute of Physics Inc., 2016. 030003 (AIP Conference Proceedings; Vol. 1742).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations

AU - Assi, I. A.

AU - Bahlouli, H.

AU - Alhaidari, A. D.

PY - 2016/6/10

Y1 - 2016/6/10

N2 - The aim of this research is to extend the class of solvable potentials of Dirac equation as a continuation to the work in [1]. We expand the spinor wavefunction in a square integrable spinor basis functions in which the expansion coefficients are functions of energy and potential parameters. Requiring the wave operator, J = H - E, to be tridiagonal and symmetric, this transforms the wave equation to a three-term recursion relation for the expansion coefficients which can be solved using known mathematical results on orthogonal polynomials. For illustration, we restricted ourselves here to the so-called Laguerre basis and considered situations where the obtained recursion relations can be easily compared to the ones associated with a well-known class of orthogonal polynomials.

AB - The aim of this research is to extend the class of solvable potentials of Dirac equation as a continuation to the work in [1]. We expand the spinor wavefunction in a square integrable spinor basis functions in which the expansion coefficients are functions of energy and potential parameters. Requiring the wave operator, J = H - E, to be tridiagonal and symmetric, this transforms the wave equation to a three-term recursion relation for the expansion coefficients which can be solved using known mathematical results on orthogonal polynomials. For illustration, we restricted ourselves here to the so-called Laguerre basis and considered situations where the obtained recursion relations can be easily compared to the ones associated with a well-known class of orthogonal polynomials.

UR - https://www.scopus.com/pages/publications/84984549488

U2 - 10.1063/1.4953124

DO - 10.1063/1.4953124

M3 - Conference contribution

AN - SCOPUS:84984549488

T3 - AIP Conference Proceedings

BT - Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016

A2 - Mahdy, Abdelrahman

A2 - Can, Nurdogan

A2 - Al-Kamli, Ali

A2 - Fadhali, Mohamed

A2 - Souadi, Galib Omar

A2 - Mahgoub, Mahmoud

PB - American Institute of Physics Inc.

ER -

Assi IA, Bahlouli H, Alhaidari AD. Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations. In Mahdy A, Can N, Al-Kamli A, Fadhali M, Souadi GO, Mahgoub M, editors, Proceedings of the 5th Saudi International Meeting on Frontiers of Physics, SIMFP 2016. American Institute of Physics Inc. 2016. 030003. (AIP Conference Proceedings). doi: 10.1063/1.4953124

Solvable potentials for the 1D Dirac equation using the tridiagonal matrix representations

Abstract

Publication series

Bibliographical note

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this