Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background

In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a $\delta$ function contribution to the full Hamiltonian, which comes from the Zeeman interaction. The inclusion of spin effects leads to results which confirm a modified dynamics. Based on the self-adjoint extension method, we determined the most relevant physical quantities, such as energy spectrum, wave functions and the self-adjoint extension parameter by applying boundary conditions allowed by the system.Comment: 9 pages, 2 figures, published versio

Remarks on the Dirac oscillator in (2+1)(2+1) dimensions

In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of $sm$. In an additional analysis, we also show that an isolated bound state solution, excluded from Sturm-Liouville problem, exists.Comment: 5 pages, 2 figures, minor corrections, published versio

The 2D κ\kappa-Dirac oscillator

In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra is considered. The problem is formulated using the $\kappa$-deformed Dirac equation. The resulting theory reveals that the energies and wave functions of the oscillator are modified by the deformation parameter.Comment: 4 pages, 2 figures, Accepted for publication in Physics Letters

The DKP oscillator with a linear interaction in the cosmic string space-time

We study the relativistic quantum dynamics of a DKP oscillator field subject to a linear interaction in cosmic string space-time in order to better understand the effects of gravitational fields produced by topological defects on the scalar field. We obtain the solution of DKP oscillator in the cosmic string background. Also, we solve it with an ansatz in presence of linear interaction. We obtain the eigenfunctions and the energy levels of the relativistic field in that background.Comment: 14 pages, no figure, comments are welcom

Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys. Rev. Lett. \textbf{100}, 230403 (2008)) and describe the surface with non-trivial curvature in terms of linear defects such as dislocations and disclinations. Expressions for the modified phase shift, S--matrix and scattering amplitude are determined by applying a suitable boundary condition at the origin, which comes from the self-adjoint extension theory. We also discuss the presence of a bound state obtained from the pole of the S--matrix. Finally, we claim that the bound state, the additional scattering and the dependence of the scattering amplitude with energy are solely due to the curvature effects.Comment: 9 pages, 1 figur