In this work, the thermodynamic property of pseudoharmonic potential in the presence of external magnetic and AB fields is investigated. We used effective Boltzmann factor within the superstatistics formalism to obtain the thermodynamic properties such as Helmholtz free energy (F), Internal energy (U), entropy(S) and specific heat (C) of the system. In addition, we discuss the result of the thermodynamic properties of some selected diatomic molecules of 2 2 2 ,, N Cl I and CH using their experimental spectroscopic parameters and that of the variation of the deformation parameter of 0,0.3,0.7 q  . We also illustrated with some graphs for clarity of our results in both cases.

The Deng-Fan-Eckart (DFE) potential is as good as the Morse potential in studying atomic interaction in diatomic molecules. By using the improved Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this adopted molecular model via the Factorization Method. With the energy equation obtained, the thermodynamic properties of some selected diatomic molecules(2 H , CO , ScN and ScF) were obtained using Poisson summation method.. The unnormalized wave function is also derived. The energy spectrum for a set of diatomic molecules for different values of the vibrational n and rotational are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the Deng-Fan potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods.

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In this research, the radial Schrodinger equation for a newly proposed screened Kratzer-Hellmann potential model was studied via the conventional Nikiforov-Uvarov method. The approximate bound state solution of the Schrodinger equation was obtained using the Greene-Aldrich approximation in addition to the normalized eigenfunction for the new potential model, both analytically and numerically. These results were employed to evaluate the rotational-vibrational partition function and other thermodynamic properties for the screened Kratzer-Hellmann potential. The results obtained have been graphically discussed. Also, the normalized eigenfunction has been used to calculate some information-theoretic measures including Shannon entropy and Fisher information for low lying states in both position and momentum spaces numerically. The Shannon entropy results obtained agreed with the Bialynicki-Birula and Mycielski inequality, while the Fisher information results obtained agreed with the Stam, Crammer-Rao inequality. Also, an alternating increasing and decreasing localization across the screening parameter for both eigenstates were observed.