Exact solutions of [Formula: see text]-dependent Schrödinger equation with quantum pseudo-harmonic oscillator and its applications for the thermodynamic properties in normal and superstatistics.

The effects of the curvature parameters on the energy eigenvalues and thermodynamic properties of quantum pseudoharmonic oscillator are investigated within the framework of nonrelativistic quantum mechanics. By employing Nikiforov-Uvarov method, the energy spectra are obtained and used to study the ordinary statistics and q-deformed superstatistics as a function of temperature in the presence and absence of the curvature parameters. It is shown that the q-deformed supertatistics properties of the quantum pseudoharmonic oscillator reduce to the ordinary statistical properties in the absence of the deformation parameter. Finally, our results are illustrated graphically to show the behaviour of the energy spectra and thermodynamic properties for the three curvature parameters:[Formula: see text].

Approximate energy spectra of improved generalized Mobius square potential (IGMSP) for some diatomic hydride molecules.

By employing the dissociation energy and equilibrium bond length as explicit parameters, we obtained the improved generalized Mobius square potential (IGMSP) model. We also defined the IGMSP parameters in terms of the molecular spectroscopic parameters. The IGMSP has been used to model inter-nuclear interaction potential curves for different diatomic hydrides. Furthermore, we have obtained the ro-vibrational energy spectra of the IGMSP model, both analytically and numerically for the selected diatomic hydrides. This was done by employing a Pekeris-type approximation scheme and an appropriate coordinate transformation to solve the Schrodinger equation. Our results have been compared with the experimental Rydberg-Klein-Rees (RKR) data points and the results of Morse potential. We calculated the mean absolute percentage deviation of IGMSP from the experimental RKR data points for the selected diatomic hydrides and that of Morse potential. The effects of the potential parameters, including the vibrational and rotational quantum numbers on the ro-vibrational energies for the different diatomic hydrides, have also been discussed. This study has shown to be highly relevant to the studies of thermodynamic and thermochemical functions of diatomic molecules.

Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties.

We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene-Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.