Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

Highlights: • Solutions of Schrödinger equation in the presence of Pöschl–Teller potential is obtained. • Solutions of Dirac equation in the presence of Pöschl–Teller potential is obtained. • Rotational and vibrational energy eigenvalues of some diatomic molecules are calculated. • Thermodynamics properties of some diatomic molecules are obtained. - Abstract: We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl–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 Schrödinger system. Rotational and 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