Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov–Uvarov method

Abstract

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, b $$ \overline{\mathrm{c}}, $$ and c $$ \overline{\mathrm{s}} $$ 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.