Abstract
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number n. Some particular cases which lead to known physical systems are also addressed.
Highlights
Interesting issues that should be investigated with the insertion of the couplings in the Dirac equation are the socalled the spin and the pseudo-spin symmetries [3]
We have studied the dynamics of a 2D Dirac oscillator interacting with cylindrically symmetric scalar and vector potentials in the space-time of the cosmic string
We used an appropriate ansatz for the Dirac equation and obtained a system of coupled first order differential equations
Summary
Interesting issues that should be investigated with the insertion of the couplings in the Dirac equation are the socalled the spin and the pseudo-spin symmetries [3]. We analyze in details the solutions of the Dirac equation with both scalar and vector interactions under the spin and the pseudo-spin symmetry limits in the cosmic string spacetime [57]. [71, 72]), where the spin and pseudospin symmetries in the relativistic mean field with a deformed potential are investigated In this context, a relation between the deformed wave function and the spherical wave function was established at the spherical limit by using the transformation from the cylindrical coordinate into the polar coordinate. A relation between the deformed wave function and the spherical wave function was established at the spherical limit by using the transformation from the cylindrical coordinate into the polar coordinate This relationship enables us to investigate the inclusion of cylindrical symmetrical potentials in the Dirac equation in other scenarios, such as the cosmic string.
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