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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 7, p.633-641


Antia A.D., Ituen E.E.

Theoretical Physics Group, Department of Physics, Faculty of Science, University of Uyo
(Nigeria; e-mail: antiacauchy@yahoo.com, akaninyeneantia@uniuyo.edu.ng)

Nonrelativisitic Treatment of Schrödinger Particles under Inversely Quadratic Hellmann Plus Ring-Shaped Potential

Section: General Problems of Theoretical Physics
Original Author's Text:  English

Abstract: We have solved approximately the Schr¨odinger equation with the inversely quadratic Hell-
mann plus ring-shaped potential in the framework of the Nikiforov–Uvarov method. The energy
eigenvalues and corresponding wave functions of the radial and angular parts are obtained in
terms of Jacobi polynomials. In special cases, our result reduces to the cases of three well-
known potentials such as the Coulomb potential, inversely quadratic Yukawa potential, and
Hartman potential. The energy eigenvalues are evaluated as well. Our numerical results can
be useful for other physical systems.

Key words: Schr¨odinger wave equation, inversely quadratic Hellmann potential, ring-shaped
potential, Nikiforov–Uvarov method, approximation scheme.