Bound state solutions of the generalized shifted Hulthén potential

Abstract

In this study, we obtain an approximate solution of the Schrödinger equation in arbitrary dimensions for the generalized shifted Hulthén potential model within the framework of the Nikiforov–Uvarov method. The bound state energy eigenvalues were computed, and the corresponding eigenfunction was also obtained. It is found that the numerical eigenvalues were in good agreement for all three approximations scheme used. Special cases were considered when the potential parameters were altered, resulting in Hulthén potential and Woods–Saxon Potential, respectively. Their energy eigenvalues expressions agreed with the already existing literature. A straightforward extension to the s-wave case for Hulthén potential and Woods–Saxon potential cases is also presented.