https://doi.org/10.1140/epjc/s10052-019-7115-7
Regular Article - Theoretical Physics
On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries
1
Departamento de Física, Universidade Federal do Maranhão, São Luís, MA, 65085-580, Brazil
2
Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, 84030-900, Brazil
3
Departamento de Física, Universidade Federal de Lavras, Caixa Postal 3037, Lavras, MG, 37200-000, Brazil
* e-mail: fmandrade@uepg.br
Received:
1
December
2018
Accepted:
5
July
2019
Published online:
15
July
2019
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.
© The Author(s), 2019
