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 and other thermodynamic properties such as vibrational free energy, , vibrational internal energy, , vibrational entropy, , and vibrational specific heat, are presented. We also discuss special cases of this potential. Our result is consistent with previous studies in the literature.