Any[states solutions of the Schr€odinger equation interacting withHellmann-generalized Morse potential model

Abstract

The approximate analytical solutions of the radial Schrӧdinger equation have been obtained with a newly proposed potentialcalled Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential and generalized Morse orDeng-Fan potential. The Hellmann-generalized Morse potential actually comprises of three different potentials which includesYukawa 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 parametricNikiforov-Uvarov method. The energy equation for some potentials such as Deng-Fan, Rosen Morse, Morse, Hellmann, Yukawaand Coulomb potentials have also been obtained by varying some potential parameters. Some numerical results have beencomputed. We have plotted the behavior of the energy eigenvalues with different potential parameters and also reported on thenumerical result. Finally, we computed the variance and information energy for the Hellmann-generalized Morse potential.