Minimal length corrections to quantum bound states of an energy-dependent Coulomb potential in global monopole spacetime

We present quasi-exact analytical solutions of the Schrödinger equation in the spacetime of a global monopole, incorporating minimal length effects via the Generalized Uncertainty Principle (GUP). Two Coulomb-type interactions are considered: the standard form and an energy-dependent variant, characterized by the parameter a controlling the strength of the energy dependence. The GUP is encoded by the deformation parameter [Formula: see text], which sets the minimal length scale. Our results show that spacetime curvature and minimal length effects induce non-trivial shifts in the bound-state spectrum. While theoretical consistency requires [Formula: see text], compatible with existing experimental bounds ([Formula: see text]–[Formula: see text]), the presence of curvature can further tighten this limit, with [Formula: see text] possible for sufficiently curved geometries. These findings demonstrate that the interplay between spacetime topology and potential structure imposes significant constraints on the allowed range of the GUP parameter, highlighting new connections between topological defects, quantum geometry, and minimal-length phenomenology.