Extensões auto-adjuntas e suas aplicações no Efeito Aharonov-Bohm

Abstract

This work presents a review of theoretical approaches related to the quantum behavior of particles subjected to the Aharonov–Bohm effect, highlighting the role of electromagnetic potentials in determining the physical properties of the system. Both traditional formulations and some more recent methods are addressed, particularly those based on self-adjoint extensions of operators, which enable a rigorous treatment of singular Hamiltonians. Among these methods, the Bulla–Gesztesy theorem stands out, providing a solid mathematical framework for defining the domain of the involved operators. Furthermore, the anomalous magnetic moment is incorporated into the system modeling, representing a correction in relation to conventional approaches. The analysis is also extended to quantum structures confined in conical spaces, where the geometry of the space may influence the Hamiltonian spectrum. The review indicates that the choice of the extension parameter λm is relevant for the characterization of bound states and for the description of the quantum dynamics of the studied model.