Download Dirac And Klein-Gordon Equations With Equal Scalar

Dirac And Klein-Gordon Equations With Equal Scalar And
Vector Potentials
Alhaidari, AD; Bahlouli, H; Al-Hasan, A
ELSEVIER SCIENCE BV, PHYSICS LETTERS A; pp: 87-97; Vol: 349
King Fahd University of Petroleum & Minerals
http://www.kfupm.edu.sa
Summary
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. (c) 2005 Elsevier
B.V. All rights reserved.
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©
Copyright: King Fahd University of Petroleum & Minerals;
http://www.kfupm.edu.sa
For pre-prints please write to: [email protected]; [email protected];
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©
Copyright: King Fahd University of Petroleum & Minerals;
http://www.kfupm.edu.sa