Dirac and Klein Gordon equations with equal scalar and vector potentials

By A. Alhaidari, H. Bahlouli, A. Al-Hasan. 2005

267 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/43aa9c1a8a99fd0b9289bc98b075617b7cfd279f

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In Atomic and Molecular Physics, and Optics

  1. Shan-Gui Zhou
  2. Haozhao Liang
  3. Jie Meng

In Statistical and Nonlinear Physics

  1. Shan-Gui Zhou
  2. Jie Meng

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