A Variational Approach for Numerically Solving the Two-Component Radial Dirac Equation for One-Particle Systems

Antonio L. A. Fonseca, Daniel L. Nascimento, Fabio F. Monteiro, Marco A. Amato

Faculdade UnB Planaltina, University of Brasília, Brasília, Brazil.
Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil.

DOI: 10.4236/jmp.2012.34048                

Abstract

In this paper we propose a numerical approach to solve the relativistic Dirac equation suitable for computational calculations of one-electron systems. A variational procedure is carried out similar to the well-known Hylleraas computational method. An application of the method to hydrogen isoelectronic atoms is presented, showing its consistency and high accuracy, relative to the exact analytical eigenvalues.

Keywords

One-Electron Systems; 2D Dirac Equation; No-Inertial Frames; Variational Approach

Conflicts of Interest

The authors declare no conflicts of interest.

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