Relativistic treatment of the spin-zero particles subject to the second Pöschl–Teller-like potential

The three-dimensional Klein-Gordon equation is solved for the case of equal vector and scalar second Pöschl–Teller potential by proper approximation of the centrifugal term within the framework of the asymptotic iteration method. Energy eigenvalues and the corresponding wave function are obtained analytically. Eigenvalues are computed numerically for some values of n and l. It is found that the results are in good agreement with the findings of other methods for short-range potential.