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A Variational Approach for Numerically Solving the Two-Component Radial Dirac Equation for One-Particle Systems
Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
Faculdade UnB Planaltina, University of Brasília, Brasília, Brazil
Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
- 1 Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
- 2 Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
- 3 Faculdade UnB Planaltina, University of Brasília, Brasília, Brazil
- 4 Institute of Physics and International Center for Condensed Matter, University of Brasília, Brasília, Brazil
Journal of Modern Physics·Volume 03 (2012)·Pages 350–354·Published 27 April 2012·DOI10.4236/jmp.2012.34048
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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.
KeywordsOne-Electron Systems2D Dirac EquationNo-Inertial FramesVariational Approach
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