Solutions of the Schrödinger equation under topological defects space-times and generalized uncertainty principle

We study the behavior of non-relativistic quantum particles interacting with the linear potential plus the Coulomb potential (LCP) and Kratzer potential under the generalized uncertainty principle (GUP) and the cosmic string space-time. By using the functional Bethe ansatz method, we give closed-form solutions for the energies and the wave functions. The allowed potential parameters have been discussed and the corresponding constraint equations have been obtained.