Klein–Gordon Equation and Nonrelativistic Thermodynamic Properties with Improved Screened Kratzer Potential

By employing the concept of the newly proposed Nikiforov-Uvarov functional analysis (NUFA) method, we solved the Klein–Gordon equation with the improved screened Kratzer potential (ISKP) model. The analytical expressions of the energy eigensolutions and numerical results were obtained for different diatomic molecules, both at the relativistic and nonrelativistic limits. Variation of the energy eigenvalues with potential parameters and quantum numbers was also discussed. In addition, the effects of temperature and upper bound vibration quantum number on the vibrational partition function and other thermodynamic functions have been discussed. Different special cases have been obtained from the ISKP, which correspond to the results in literatures. It was observed that the control parameter of ISKP has a great effect on the energy eigenvalues obtained.