Thermophysical Properties and Mass Spectra of Meson Systems via the Nikiforov–Uvarov Method

Abstract In this study, we analyze the mass spectra of meson systems within an N-dimensional space using the Killingbeck potential combined with an inversely quadratic potential. We employ the Nikiforov–Uvarov method along with the Pekeris approximation scheme to account for the centrifugal barrier. This approach enables us to compute numerical energy eigenvalues, normalized eigenfunctions, and mass spectra for both heavy and heavy–light meson systems. We explore various scenarios of the potential and find that the resulting energy eigenvalues are consistent with those obtained through previous analytical methods and experimental data. Additionally, we compute the thermodynamic properties of quarkonium particles, including mean energy, specific heat, free energy, and entropy. Furthermore, we investigate the effects of temperature and the dimensional number on meson masses and thermodynamic properties, providing valuable insights into the behavior of meson systems under different conditions.