Thermodynamic properties of heavy mesons are calculated within the framework of
the N-dimensional radial Schrödinger equation. The Cornell potential is extended by
including the quadratic potential plus the inverse of quadratic potential. The energy
eigenvalues and the corresponding wave functions are calculated in the N-dimensional
space using the Nikiforov–Uvarov (NU) method. The obtained results are applied for
calculating the mass of spectra of charmonium, bottomonium, bc; and cs mesons. The
thermodynamic properties of heavy quarkonia such as the mean energy, the specific
heat, the free energy, and the entropy are calculated. The effect of temperature and the
dimensionality number on heavy meson masses and thermodynamic properties is
investigated. The obtained results are improved in comparison with other theoretical
approaches and in a good agreement with experimental data. We conclude that the
present potential well describes thermodynamic properties in the three-dimensional
space and also the higher dimensional space.