Relativistic quantum motions of spin-0 scalar particles in point-like defect under modified Woods–Saxon potential

In this study, we investigate the Klein–Gordon equation within the context of a point-like global monopole subjected to a modified Woods–Saxon potential. The presence of a global monopole introduces a topological defect in the space-time fabric, which significantly influences the behavior of scalar charged particles. Our primary objective is to derive the exact analytical solution of the Klein–Gordon equation, explore the relativistic energy eigenvalues and wave function, and examine the impact of global monopole, the modified Woods–Saxon potential as well as flux field on the quantum particles. By integrating these elements, we provide a comprehensive analysis of how the topological defect, flux field and the potential shape the dynamics of the scalar charged particles, yielding insights into the interplay between geometric and potential effects in such a quantum system.