Eigensolution and various properties of the screened cosine Kratzer potential in D dimensions via relativistic and non-relativistic treatment

Abstract

In this article, we proposed screened cosine Kratzer potential (SCKP). Using approximation suggested by Greene–Aldrich, the approximate bound-state solutions of the D-dimensional Klein–Gordon equation for SCKP have been obtained via the generalized Nikiforov–Uvarov method. The bound-state energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric functions were obtained. From the proposed SCKP model, we recovered different potentials such as screened Kratzer potential, standard Kratzer potential, generalized cosine Yukawa potential, screened Coulomb potential, Coulomb potential, inversely quadratic Yukawa potential and its corresponding energy eigenvalues from obtained energy eigenvalues of the SCKP in both the relativistic and non-relativistic regime. We obtained rotational–vibrational energy for few heterogeneous (LiH, HCl, NO) and homogeneous (H$_2$, I$_2$, O$_2$) diatomic molecules in three dimensions. The numerical results obtained for LiH, HCl, NO and I$_2$, O$_2$ diatomic molecules are in very good agreement with the results previously obtained by others. We obtained various properties of the SCKP such as thermodynamical properties (partition function, vibrational mean energy, vibrational mean free energy, vibrational specific heat capacity and vibrational entropy, information energy $E(\gamma )$, Tsallis entropy T(q), Rényi entropy R(q), Shannon entropy $S(\gamma )$ and Fisher information entropy $I(\gamma )$) using energy eigenvalues and eigenfunctions, the expressions for the expectation values of the square of inverse of position $1/r^2$, inverse of position 1/r, kinetic energy T, and square of momentum $p^2$ via Hellmann–Feynman theorem. We also presented quarkonium mass spectroscopy using energy eigenvalues of the SCKP.