Dirac and Klein-Gordon equations with equal scalar and vector potentials

A. D. Alhaidari; H. Bahlouli; A. Al-Hasan

doi:10.1016/j.physleta.2005.09.008

Dirac and Klein-Gordon equations with equal scalar and vector potentials

A. D. Alhaidari^*
, H. Bahlouli
, A. Al-Hasan

^*Corresponding author for this work

Department of Physics

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

314 Scopus citations

Abstract

We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating interest. We consider a large class of these problems in which the potentials are noncentral (angular-dependent) such that the equations separate completely in spherical coordinates. The relativistic energy spectra are obtained and shown to differ from those of well-known problems that have the same nonrelativistic limit. Consequently, such problems should not be misinterpreted as the relativistic extension of the given potentials despite the fact that the nonrelativistic limit is the same. The Coulomb, oscillator and Hartmann potentials are considered. Additionally, we investigate the Klein-Gordon equation with uneven mix of potentials leading to the correct relativistic extension. We consider the case of spherically symmetric exponential-type potentials resulting in the S-wave Klein-Gordon-Morse problem.

Original language	English
Pages (from-to)	87-97
Number of pages	11
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	349
Issue number	1-4
DOIs	https://doi.org/10.1016/j.physleta.2005.09.008
State	Published - 9 Jan 2006

Bibliographical note

Funding Information:
Bahlouli acknowledges the support of King Fahd University of Petroleum and Minerals. Al-Hasan is grateful to the Physics Department at King Faisal University for support. Fruitful discussions with M.S. Abdelmonem are highly appreciated.

Keywords

Dirac equation
Klein-Gordon equation
Morse potential
Pseudo-spin symmetry
Scalar and vector coupling

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1016/j.physleta.2005.09.008

Cite this

@article{edaab35be3104e44b7a83a8c711b2162,

title = "Dirac and Klein-Gordon equations with equal scalar and vector potentials",

abstract = "We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating interest. We consider a large class of these problems in which the potentials are noncentral (angular-dependent) such that the equations separate completely in spherical coordinates. The relativistic energy spectra are obtained and shown to differ from those of well-known problems that have the same nonrelativistic limit. Consequently, such problems should not be misinterpreted as the relativistic extension of the given potentials despite the fact that the nonrelativistic limit is the same. The Coulomb, oscillator and Hartmann potentials are considered. Additionally, we investigate the Klein-Gordon equation with uneven mix of potentials leading to the correct relativistic extension. We consider the case of spherically symmetric exponential-type potentials resulting in the S-wave Klein-Gordon-Morse problem.",

keywords = "Dirac equation, Klein-Gordon equation, Morse potential, Pseudo-spin symmetry, Scalar and vector coupling",

author = "Alhaidari, \{A. D.\} and H. Bahlouli and A. Al-Hasan",

note = "Funding Information: Bahlouli acknowledges the support of King Fahd University of Petroleum and Minerals. Al-Hasan is grateful to the Physics Department at King Faisal University for support. Fruitful discussions with M.S. Abdelmonem are highly appreciated.",

year = "2006",

month = jan,

day = "9",

doi = "10.1016/j.physleta.2005.09.008",

language = "English",

volume = "349",

pages = "87--97",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier BV",

number = "1-4",

}

TY - JOUR

T1 - Dirac and Klein-Gordon equations with equal scalar and vector potentials

AU - Alhaidari, A. D.

AU - Bahlouli, H.

AU - Al-Hasan, A.

N1 - Funding Information: Bahlouli acknowledges the support of King Fahd University of Petroleum and Minerals. Al-Hasan is grateful to the Physics Department at King Faisal University for support. Fruitful discussions with M.S. Abdelmonem are highly appreciated.

PY - 2006/1/9

Y1 - 2006/1/9

N2 - We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating interest. We consider a large class of these problems in which the potentials are noncentral (angular-dependent) such that the equations separate completely in spherical coordinates. The relativistic energy spectra are obtained and shown to differ from those of well-known problems that have the same nonrelativistic limit. Consequently, such problems should not be misinterpreted as the relativistic extension of the given potentials despite the fact that the nonrelativistic limit is the same. The Coulomb, oscillator and Hartmann potentials are considered. Additionally, we investigate the Klein-Gordon equation with uneven mix of potentials leading to the correct relativistic extension. We consider the case of spherically symmetric exponential-type potentials resulting in the S-wave Klein-Gordon-Morse problem.

AB - We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating interest. We consider a large class of these problems in which the potentials are noncentral (angular-dependent) such that the equations separate completely in spherical coordinates. The relativistic energy spectra are obtained and shown to differ from those of well-known problems that have the same nonrelativistic limit. Consequently, such problems should not be misinterpreted as the relativistic extension of the given potentials despite the fact that the nonrelativistic limit is the same. The Coulomb, oscillator and Hartmann potentials are considered. Additionally, we investigate the Klein-Gordon equation with uneven mix of potentials leading to the correct relativistic extension. We consider the case of spherically symmetric exponential-type potentials resulting in the S-wave Klein-Gordon-Morse problem.

KW - Dirac equation

KW - Klein-Gordon equation

KW - Morse potential

KW - Pseudo-spin symmetry

KW - Scalar and vector coupling

UR - https://www.scopus.com/pages/publications/29544437042

U2 - 10.1016/j.physleta.2005.09.008

DO - 10.1016/j.physleta.2005.09.008

M3 - Article

AN - SCOPUS:29544437042

SN - 0375-9601

VL - 349

SP - 87

EP - 97

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-4

ER -

Dirac and Klein-Gordon equations with equal scalar and vector potentials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this