Approximate Bound State Solutions of the Hellmann Plus Kratzer Potential in N-dimensional Space

Abstract

We have examined the approximate 𝑙𝑁−1-state solutions of the N-dimensional Schrödingerequation for a particle interacting with the Hellmann plus Kratzer potential. Inhyperspherical coordinate system, we have constructed the bound state energy equation andthe wavefunctions expressed by the hypergeometric function via the asymptotic iterationapproach in detail. When considered the special cases of parameters in Hellmann plusKratzer potential, this potential turns into several potential models. In this connection, thenon-relativistic energy spectra for the modified Kratzer, Yukawa, Coulomb and Hellmannpotentials in approximate analytic form have been obtained in hyperspherical coordinates.We have presented the numerical energy eigenvalues for the Hellmann, Yukawa andCoulomb potentials in 𝑁 = 3 dimensions. Our present results provide an appropriate test ofthe accuracy of asymptotic iteration formalism.