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/(2α))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.