Nonrelativistic solutions of Schrödinger equation and thermodynamic properties with the proposed modified Mobius square plus Eckart potential.

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.

Dirac equation and thermodynamic properties with the Modified Kratzer potential.

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.