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The solutions of the Schrὅdinger equation for a molecular Mobius square potential are obtained using two elegant traditional methods. In each case, the energy equation is obtained. The pure vibrational energies for seven different molecules are studied using their respective spectroscopic constants and the obtained energy equation. The present results are compared with the standard results and the results of other potential models. The present study shows that the molecular Mobius square potential produces better results compared to some potential models. [ABSTRACT FROM AUTHOR]

A Kratzer‐Fues potential is coupled with its self to form a double Kratzer‐Fues potential. The solutions of the radial Schrödinger equation with the combined potential are obtained via two different methodologies. Using the supersymmetric approach, the energy equation for a non‐approximated centrifugal term is obtained. The energy equation for the approximated centrifugal term is obtained using the parametric Nikiforov‐Uvarov method. Numerical results are computed for five molecules using MATLAB software program. The computed numerical values are compared with the experimental values and the ground state energy obtained from Herzberg's energy level equation. The study revealed that the results of the approximated centrifugal term are better than the results of the non‐approximated centrifugal term for four molecules. [ABSTRACT FROM AUTHOR]

In this paper, we obtained the non-relativistic ro-vibrational energy spectra, constants, expectation values and the thermodynamic properties of the Schiöberg potential function within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method. We applied an improved Greene-Aldrich-type approximation scheme to the orbital centrifugal term and obtained a closed-form energy equation. The energy eigenvalues obtained numerically are in excellent agreement with other analytical and numerical works in the literature. The results for the expectation values confirm the principle of energy conservation. The results in this present work reinforce the exactness of the leading order WKB approximation and may also be of interest to researchers in the field of molecular and chemical physics. [ABSTRACT FROM AUTHOR]

In this work, we determined an approximate eigen solutions of Modified multi-parameter exponential potential using supersymmetric quantum mechanics approach (SUSY) with improved Greene-Aldrich approximation to the centrifugal term. The energy equation and its corresponding normalised radial wave function were fully obtained. The proposed potential reduces to other useful potentials like Rosen-Morse, Hellmann, Yukawa and Coulomb potential as special cases. The thermodynamic properties like the vibrational mean energy ( U β , V ), Vibrational heat capacity ( C β , V ), vibrational entropy ( S β , V ) and vibrational free energy ( F β , V ) of the interacting potential were studied via partition function ( Z β , V ) obtained from the resulting energy equation. This study was applied to three diatomic molecules: Chromium hydride (CrH), Titanium Hydride (TiH) and Thiocynate (ScN). To ascertain the high degree of our analytical mathematical accuracy, we compared the results of special cases with an existing results. These were found to be in excellent agreement with the existing results., Competing Interests: The authors declare no conflict of interest., (© 2022 The Author(s).)