Thermodynamic properties and approximate solutions of the ℓ-state Pöschl-Teller-type potential

In this study, the solutions of the ℓ-state Pöschl-Teller-type potential for the Schrödinger and Klein-Gordon equations are obtained using the parametric Nikiforov-Uvarov method. Solving the Schrödinger and Klein-Gordon wave equations, the energy eigenvalues and wave functions are obtained. For the case ℓ=0, we made comparison with previous results where the solutions of Schrödinger equation for the Pöschl-Teller-type potential were obtained for s-wave (ℓ=0) state. We also obtain the thermodynamic properties such as vibrational mean energy, vibrational specific heat, vibrational mean free energy and vibrational entropy for the Pöschl-Teller-type potential in the classical limit.