Non-relativistic quantum dynamics in Born-Infeld gravity inspired by Eddington spacetime global monopole

In this work, we investigate the quantum dynamics of non-relativistic systems in a Born-Infeld spacetime. We analyze some general scenarios, which concerns the effects of a harmonic oscillator and an inverse square-type potential as well as an Aharonov-Bohm geometric phase. We obtain an analytical solution for the most general case in terms of a confluent Heun function and define the energy spectrum by referring to the ground state, together with its respective eigenfunction. A graphical representation was built so that it was possible to visualize some of the possible energy configurations. For negative values of the Born-Infeld parameter epsilon < 0, we perform a connection with results of quantum dynamics already investigated in the literature for the Ellis-Bronnikov spacetime.