A 2D spinless version of Dirac's equation written in a noninertial frame of reference

Authors

  • D. L. Nascimento,

    1. Institute of Physics and International Center for Condensed Matter Physics, University of Brasília, 70919-970 Brasília-DF, Brazil
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  • A. L. A. Fonseca

    Corresponding author
    1. Institute of Physics and International Center for Condensed Matter Physics, University of Brasília, 70919-970 Brasília-DF, Brazil
    • Institute of Physics and International Center for Condensed Matter Physics, University of Brasília, 70919-970 Brasília-DF, Brazil
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Abstract

In this article, we present a quantized classical-like wave equation. It is obtained by considering the equivalence between the Hamilton-Jacobi eq. (which belongs to the usual manifold \input amssym ${\Bbb R^{3}} \otimes {\Bbb R} $ of General Relativity), with our two spinor versions of the Dirac eq. (which belongs to the associated complex manifold \input amssym ${\Bbb C}\otimes {\Bbb C} $). In which the electron is considered as a particle-like entity, instead of the usual wave-like interpretation of standard Quantum Mechanics. We also consider the transformation properties between the two manifolds through the corresponding groups O(3,1) and SU(2), but we assume a flat Minkowsky space as the background space. We made an illustrative application to the rather standard problem of the hydrogen and helium atoms. We propose a variational extension of the approach, through a Hylleraas-like computational method, to take into account a many electron problem too futurely. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

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