Approximate solutions and determination of the thermodynamic properties of the generalized Yukawa potential using extended Nikiforov–Uvarov method

In this study, the approximate analytical bound state solutions with a newly proposed generalized Yukawa potential are solved using the extended Nikiforov–Uvarov method with the help of Greene–Aldrich approximation to the centrifugal term. The corresponding wave function is expressed in terms of the confluent Heun function. The numerical bound state solutions are reported for various values of the screening parameter and orbital angular quantum number. Furthermore, the bound state energy spectrum is used to study the thermodynamic properties of the system comprehensively, and we have discussed the influence of inverse temperature and maximum quantum number on the thermodynamic properties.