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

Abstract

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.