Quantum Spectral Analysis of Non-Relativistic Particles in Schwarzschild Spacetime under the Aharonov–Bohm Effect and External Potentials

Abstract This study presents a semi-classical, non-relativistic quantum-mechanical analysis of bound-state spectra for a scalar particle in Schwarzschild spacetime, incorporating both external potentials and the Aharonov–Bohm (AB) effect. By reformulating the radial Schrödinger equation via the Rindler approximation and introducing the AB flux as a prescribed gauge potential, we derive analytical expressions for the energy eigenvalues under Coulomb and Mie-type confinement. The results reveal a rich interplay between spacetime curvature, topological phase contributions, and short-range potential structure. Specifically, increasing the Schwarzschild radius leads to a redshift and compression of energy levels, with curvature-induced terms eventually dominating the confinement landscape. The AB flux induces a tunable spectral shift through its modification of the effective angular momentum, though this effect remains secondary to gravitational curvature. The effective potential analysis illustrates how curvature and gauge phases combine to shape quantum bound states. While idealized, this model offers insights into the sensitivity of quantum spectra to geometry and topology, with potential relevance for analogue gravity experiments and synthetic gauge field simulations. The approach assumes a fixed background geometry and neglects backreaction and relativistic corrections, and the results should be interpreted within this approximate framework. These results find relevance in analog gravity systems, quantum simulations with synthetic gauge fields, and investigations of black hole-modified quantum systems.