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

Abstract

AbstractIn 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