  We apply the asymptotic iteration method (AIM) to obtain the solutions of
Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also
obtain the solutions of Dirac equation for the same potential under the
condition of spin and pseudospin (p-spin) symmetries. We show that in the
nonrelativistic limits, the solution of Dirac system converges to that of
Schrodinger system. Rotational-Vibrational energy eigenvalues of some diatomic
molecules are calculated. Some special cases of interest are studied such as
s-wave case, reflectionless-type potential and symmetric hyperbolic PT
potential. Furthermore, we present a high temperature partition function in
order to study the behavior of the thermodynamic functions such as the
vibrational mean energy U, specific heat C, free energy F and entropy S.
