arXiv:1501.02264 [quant-ph]AbstractReferencesReviewsResources
On solutions of the Pauli equation in non-static de Sitter metrics
E. M. Ovsiyuk, K. V. Kazmerchuk
Published 2015-01-09Version 1
A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure for transition to the Pauli approximation is conducted in the equations in the variables $(t, r)$, obtained after separating the angular dependence of $(\theta, \phi)$ from the wave function. The non-relativistic systems of equations in the variables $(t, r)$ is solved exactly in both models. The constructed wave functions do not represent stationary states with fixed energy, however the corresponding probability density does not depend on the time.