On the solutions and applications of the generalised Cornell potential

Abstract

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${}_2$, I${}_2$ and H${}_2$ and the mass spectra of $b\overline{s}$ and $b\overline{q}$ mesons 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.

GRAPHICAL ABSTRACT

Keywords:

• Schrödinger equation
• generalised Cornell potential
• Nikiforov–Uvarov functional analysis method
• eigenvalue spectra
• expectation values

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

One of the author, Vinod Kumar acknowledges the University Grants Commission (UGC), New Delhi (India) for granting financial support through NFSCS – fellowship.