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A 2D spinless version of Dirac's equation written in a noninertial frame of reference
Author(s) -
Nascimento D. L.,
Fonseca A. L. A.
Publication year - 2011
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22657
Subject(s) - zitterbewegung , spinor , manifold (fluid mechanics) , dirac equation , physics , quantum mechanics , dirac (video compression format) , reference frame , mathematical physics , transformation (genetics) , wave function , classical mechanics , frame (networking) , computer science , chemistry , mechanical engineering , telecommunications , biochemistry , neutrino , engineering , gene
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