Complete solutions of the Dirac equation with q-deformed hyperbolic Pöschl-Teller potential plus a trigonometric Scarf II potential

Abstract

Under the condition of the spin symmetry, we rigorously solve the Dirac equation with the q − deformed hyperbolic Pöschl-Teller potential plus a trigonometric Scarf II potential. According to the values of the deformation parameter q, four different cases are considered. For the two cases q ≥ 1 and q ≤ − 1 with 1 2 α ln q < r < + ∞ , the analytical energy spectra and the spinor wave functions associated with the l d − wave bound states are obtained using a suitable approximation to the centrifugal potential term. When 0 < q < 1 or −1 < q < 0, the spinor wave functions for the s − wave bound states are derived and we find that the quantization conditions are transcendental equations which can be solved numerically. The special case q = 0 is also discussed.