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

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