Any ℓ−states solutions of the Schrödinger equation interacting with Hellmann-generalized Morse potential model

The approximate analytical solutions of the radial SchrÓ§dinger equation have been obtained with a newly proposed potential called Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential and generalized Morse or Deng-Fan potential. The Hellmann-generalized Morse potential actually comprises of three different potentials which includes Yukawa potential, Coulomb potential and Deng-Fan potential. The aim of combining these potentials is to have a wide application. The energy eigenvalue and the corresponding wave function are calculated in a closed and compact form using the parametric Nikiforov-Uvarov method. The energy equation for some potentials such as Deng-Fan, Rosen Morse, Morse, Hellmann, Yukawa and Coulomb potentials have also been obtained by varying some potential parameters. Some numerical results have been computed. We have plotted the behavior of the energy eigenvalues with different potential parameters and also reported on the numerical result. Finally, we computed the variance and information energy for the Hellmann-generalized Morse potential.