Analytical solutions to the Schrodinger equation for a generalized Cornell potential and its applications to diatomic molecules and heavy mesons

Here, analytical expressions of energy eigenvalues and eigen functions for a generalized Cornell potential are obtained by solving the non-relativistic Schrodinger equation using the Nikiforov-Uvarov functional analysis method along with Greene-Aldrich approximation. Energy spectra of three physically important potentials viz the pseudoharmonic, the Kratzer and the Coulomb perturbed potentials are derived from the general results. Further, within the framework of the Kratzer potential, energy eigenvalue spectra of diatomic molecules CO, NO, O-2, LiH and HCl are computed. The mass spectra of two heavy mesons are also investigated using the Coulomb perturbed potential, a form of the generalized Cornell potential. The obtained results are in good agreement with the results of others studies. The study is further extended to calculate and draw the partition function and other associated thermodynamic quantities for heavy mesons.

Automated summary

By solving the non-relativistic Schrodinger equation using the Nikiforov-Uvarov functional analysis method along with Greene-Aldrich approximation, analytical expressions of energy eigenvalues and eigen functions for a generalized Cornell potential were obtained. The energy spectra of three physically important potentials and the energy eigenvalue spectra of diatomic molecules were derived. Additionally, the mass spectra of two heavy mesons were investigated using the Coulomb perturbed potential. The study also extended to calculate thermodynamic quantities for heavy mesons.