Oscilador de Dirac bidimensional na presença de potenciais vetorial e escalar no espaço-tempo da corda cósmica: contexto das simetrias de spin e pseudospin - LIMA, Daniel França (2018)
The Dirac equation with scalar and vector couplings describing the dynamics of a twodimensionalDirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of spin and pseudo-spin symmetries. We consider in our analysis the presence of cylindrically symmetric scalar potentials which allows us to provide analytical solutions for the resultant field equation. Using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The eigenvalues of this equation are given in terms of two expressions, one being used as a quantum condition. Such a condition may be used to fix some physical parameter present in the Hamiltonian of the system but that is absent in the expression used to obtain the energy spectrum. Expressions for the energy of the oscillator are obtained for some values of the quantum number n. Some particular cases that lead to known physical systems are also investigated.