Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

A. D. Alhaidari

doi:10.1007/s10701-010-9431-5

Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

A. D. Alhaidari

King Fahd University of Petroleum & Minerals

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

23 Scopus citations

Abstract

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r² term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.

Original language	English
Pages (from-to)	1088-1095
Number of pages	8
Journal	Foundations of Physics
Volume	40
Issue number	8
DOIs	https://doi.org/10.1007/s10701-010-9431-5
State	Published - 2010

Bibliographical note

Funding Information:
Acknowledgements The support of this work by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated. We acknowledge partial support by King Fahd University of Petroleum & Minerals (KFUPM).

Keywords

Dirac equation
Eckart
Energy spectrum
Hulthén
Non-zero angular momentum
Singular potentials

ASJC Scopus subject areas

Philosophy
General Physics and Astronomy
History and Philosophy of Science

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10.1007/s10701-010-9431-5

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title = "Dirac equation with coupling to 1/r singular vector potentials for all angular momenta",

abstract = "We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulth{\'e}n and Eckart potentials.",

keywords = "Dirac equation, Eckart, Energy spectrum, Hulth{\'e}n, Non-zero angular momentum, Singular potentials",

author = "Alhaidari, \{A. D.\}",

note = "Funding Information: Acknowledgements The support of this work by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated. We acknowledge partial support by King Fahd University of Petroleum \& Minerals (KFUPM).",

year = "2010",

doi = "10.1007/s10701-010-9431-5",

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volume = "40",

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journal = "Foundations of Physics",

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T1 - Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

AU - Alhaidari, A. D.

N1 - Funding Information: Acknowledgements The support of this work by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated. We acknowledge partial support by King Fahd University of Petroleum & Minerals (KFUPM).

PY - 2010

Y1 - 2010

N2 - We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.

AB - We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.

KW - Dirac equation

KW - Eckart

KW - Energy spectrum

KW - Hulthén

KW - Non-zero angular momentum

KW - Singular potentials

UR - https://www.scopus.com/pages/publications/77954863401

U2 - 10.1007/s10701-010-9431-5

DO - 10.1007/s10701-010-9431-5

M3 - Article

AN - SCOPUS:77954863401

SN - 0015-9018

VL - 40

SP - 1088

EP - 1095

JO - Foundations of Physics

JF - Foundations of Physics

IS - 8

ER -

Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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