In the present article we solve the Dirac equation in a de Sitter universe when a constant electric field is present. Using the Bogoliubov transformations, we compute the rate of spin 1/2 created particles by the electric field. We compare our results with the scalar case. We also analyze the behavior of the density of particles created in the limit H=0, when de Sitter background reduces to a flat space-time.11.10Qr, 04.62.+v, 98.80.Cq

In the present article we have found the complete energy spectrum and the corresponding eigenfunctions of the Dirac oscillator in two spatial dimensions. We show that the energy spectrum depends on the spin of the Dirac particle.Comment: revtex, 6pp. IVIC-CFLE 93/0

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional WoodsSaxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zeroreflection condition depends on the shape of the potential.

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

Solution of the Dirac equation with pseudospin symmetry for a new harmonic oscillatory ring-shaped noncentral potential J. Math. Phys. 53, 082104 (2012) Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit J. Math. Phys. 53, 082101 (2012) Asymptotic stability of small gap solitons in nonlinear Dirac equations J. Math. Phys. 53, 073705 (2012) On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization J. Math. Phys. 53, 063503 (2012) Quasi-exact treatment of the relativistic generalized isotonic oscillatorThe method of separation of variables in the Dirac equation in the external vector fields is developed through the search for exact solutions. The essence of the method consists of the separation of the first-order matricial differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with the operator of the equations or between them is not assumed. This approach, which is perfectly justified in the presence of gravitational fields, permits one to prove rigorous theorems about necessary and sufficient conditions on the field functions that allow one to separate variables in the Dirac equation. In analogous investigations by other authors [Bagrov et al., Exact solutions of Relativistic Wave Equations (Nauka, Novosibirsk, 1982)] for electromagnetic fields an essential demand related to the operators that define the dependence of the bispinor on the separated variables is the demand for the commutation of a complete set of operators between them or with the operators of the Dirac equation. For this reason a series of possibilities that do not satisfy this demand escape the attention of these other authors. The present work liquidates this gap, solving the problem for external vector fields in general.

In this article we compute the density of scalar and Dirac particles created by a cosmological anisotropic Bianchi type I universe in the presence of a time varying electric field. We show that the particle distribution becomes thermal when one neglects the electric interaction. † Alexander von Humboldt Fellow

We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.