Study of the Dirac oscillator in the presence of vector and scalar potentials in the cosmic string space-time

Abstract

In this paper, we use the functional Bethe ansatz method to solve the radial problem of the Dirac oscillator in cosmic string space-time, and its general solution under the Killingbeck potential plus isotonic oscillator potential in the limit of the spin and the pseudo-spin symmetries are further presented. Corresponding to the expressions of energies and wave function of bound state and first excited state are given. Furthermore, some particular cases including the Cornell potential, the Kratzer potential, the Killingbeck potential and the isotonic oscillator potentials are also addressed. It shows that the energy levels of the systems depend explicitly on the potential parameters A, B, C, D, F, G and the angular deficit parameter α which characterize topological defect.