Relativistic and non-relativistic thermal properties with bound and scattering states of the Klein-Gordon equation for Mobius square plus generalized Yukawa potentials

The effects of temperature and upper bound vibrational quantum number on the thermodynamic properties of Mobius square plus generalized Yukawa potential model are investigated within the framework of both relativistic and nonrelativistic quantum mechanics using the Nikiforov-Uvarov-Functional Analysis method with Greene-Aldrich approximation to the centrifugal term. The energy eigen equation obtained for both relativistic and nonrelativistic cases were presented in a closed and compact form and applied to study partition function and other thermodynamic properties as applied to both cases. Also, the normalized wave functions of the combined potential models expressed in terms of hypergeometric function of Jacobi polynomial were studied at the ground, first and second excited states for various quantum states with various selected screening parameters. The numerical bound state solution obtained for various screening parameter increases with an increase in quantum state while the numerical scattering state solution fluctuates between small and larger numerical values with an increase in orbital angular quantum number. To ascertain the degree of accuracy of our work, the thermodynamic plots obtained for the nonrelativistic case were in excellent agreement to work of existing literature.