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This work presents the solutions to the non-relativistic Schrödinger equation for the generalised Cornell potential using the Nikiforov–Uvarov functional analysis method and the Greene–Aldrich approximation. Energy eigenvalues and eigen functions are obtained in closed form. Eigenvalue spectra of some physical potentials are also deduced from the generalised results. Further, within the framework of the Kratzer and the Coulomb perturbed potentials, two variants of the generalised potential, energy eigenvalue spectra of diatomic molecules viz CH, ScH, N, Iand Hand the mass spectra ofandmesons are determined, respectively. We also compute the expectation values of position inverse and its square, kinetic energy, and square of momentum for the above diatomic molecules by employing the Hellman–Feynman theorem. A close agreement is observed between the present results and some other past works.

On the solutions and applications of the generalised Cornell potential