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We obtain solutions of Schrödinger equation for the modified Mobius square plus Eckart (MMPSE) potential via the formula method. Numerical results are reported. In addition, the partition function Z and other thermodynamic properties such as vibrational free energy, F , vibrational internal energy, U , vibrational entropy, S , and vibrational specific heat, C are presented. We also discuss special cases of this potential. Our result is consistent with previous studies in the literature., Competing Interests: The authors declare no conflict of interest., (© 2022 The Author(s).)

The study presents approximate analytical solutions of the Schrödinger equation with a newly proposed potential model called Inversely Quadratic Hellmann-Kratzer potential (IQHKP). This potential is a superposition of Inversely Quadratic Hellman potential and Kratzer potential. The energy eigenvalues and corresponding wavefunction are calculated via the formula method. We applied our results to evaluate thermodynamic functions such as vibrational free energy, F , vibrational internal energy, U , vibrational entropy, S , and vibrational specific heat, C . We also reported special cases of importance., Competing Interests: The authors declare no conflict of interest., (© 2021 The Author(s).)

In this work, we present the analytical solutions of Dirac equation for modified Kratzer potential in the pseudospin and spin symmetry limits using the formula method. The energies of the pseudospin and spin symmetry limit are obtained analytically and numerically. The numerical values are compared with those obtained in literature. Furthermore, we study the thermodynamic properties of some diatomic molecules within the nonrelativistic spin symmetry limits., Competing Interests: The authors declare no conflict of interest., (© 2021 The Author(s).)