With the introduction of a new improved approximation scheme (Pekeris-type approximation) to deal with the centrifugal term, the energy eigenvalues and the wave functions of the Schrodinger equation of the shifted Deng-Fan molecular potential ¨ are obtained, via the asymptotic iteration method. Rotationalvibrational energy eigenvalues of some diatomic molecules are presented, these results are in good agreement with other results in the literature. For these selected diatomic molecules, energy eigenvalues obtained are in much better agreement with the results obtained from the rotating Morse potential model for moderate values of rotational and vibrational quantum numbers. Furthermore, thermodynamic properties such as the vibrational mean U, specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues are studied.

In this study, the information-theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy and Onicescu information energy are investigated analytically and numerically. The results obtained are applied to some diatomic molecules. The Renyi and Tsallis entropies are analytically obtained in position space using Srivastava-Niukkanen linearization formula in terms of the Lauricella hypergeometric function. Also they are obtained in the momentum space in terms of the multivariate Bell polynomials of Combinatorics. We observed that the Fisher information increases with n in both the position and momentum spaces, but decreases with ℓ for all the diatomic molecules considered. The Shannon entropy also increases with increasing n in the position space and decreases with increasing ℓ. The variations of the Renyi and Tsallis entropies with ℓ are also discussed. The exact and numerical values of the Onicescu information energy are also obtained, after which the ratio of information-theoretic impetuses to lengths for Fisher, Shannon and Renyi are obtained.

In this study, the solutions of the '-state Po¨schl-Teller-type potential for the Schro¨dinger and Klein-Gordon equations are obtained using the parametric Nikiforov-Uvarov method. Solving the Schro¨dinger and Klein-Gordon wave equations, the energy eigenvalues and wave functions are obtained. For the case ' ¼ 0, we made comparison with previous results where the solutions of Schro¨dinger equation for the Po¨schl-Teller-type potential were obtained for s-wave (' ¼ 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 Po¨schl-Teller-type potential in the classical limit.