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

Abstract

We have solved approximately the Schrödinger equation with the inversely quadratic Hellmann 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 wellknown 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. K e y w o r d s: Schrödinger wave equation, inversely quadratic Hellmann potential, ring-shaped potential, Nikiforov-Uvarov method, approximation scheme.

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

“…Arbitrary -solutions play a dominant role in non-relativistic quantum mechanics since the wave function and associated eigenvalues contain all the necessary information for a full description of a quantum system [5][6][7][8]. With the experimental verification of the Schrödinger equation, researchers have devoted much interest in solving the radial Schrödinger equation to obtain bound state solutions with various methods for some potential models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”