Approximate analytical solutions of the Schrödinger equation with Hulthén potential in the global monopole spacetime

In this paper, we study the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also consider that the electron is influenced by the Hulthén potential. In particular, we deal with the Schrödinger equation in the presence of a global monopole. We obtain approximate solutions for the problem, determine the scattering phase shift and the $S$-matrix, and analyze bound states.