By employing an exponential-type approximation
scheme to replace the centrifugal term, we have approximately solved the
Dirac equation for a spin-1/2 particle subjected to complex
parity–time-symmetric scalar and vector Pöschl–Teller (PT) potentials
with arbitrary spin–orbit -wave
states in view of spin and pseudospin (p-spin) symmetries. The real
bound-state energy eigenvalue equation and the corresponding two-spinor
components wave function expressible in terms of hypergeometric
functions are obtained by means of wave function analysis. The spin-
Dirac equation and the spin-0 Klein–Gordon equation with complex PT
potentials share the same energy spectrum under the choice of
(i.e. exact spin and p-spin symmetries).