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This work investigates the motion of a non-relativistic charged particlewithin the spacetime of a global monopole. We introduce the Schr\"odingerequation to describe the particle's motion with two interactions by consideringthe Kratzer and the screened modified Kratzer potential. The problem'seigenfunctions and eigenvalues are obtained by deriving and solving the radialequation. The effective potential encompasses both the Kratzer andelectrostatic self-interaction potential and leads to bound states solutions.The energy spectrum is investigated, particularly emphasizing its dependence onthe system's physical parameters. The screened modified Kratzer potential andthe screened self-interaction potential reveal an important role in influencingboth the effective potential and the energy spectrum. Additionally, it alsoaccommodates the existence of bound states. All these behaviors are illustratedwith graphs and discussed in detail.

Exact and approximate bound state solutions of the Schr\"odinger equation with a class of Kratzer-type potentials in the global monopole spacetime