  In this work, we review two methods used to approach singular Hamiltonians in
(2+1) dimensions. Both methods are based on the self-adjoint extension
approach. It is very common to find singular Hamiltonians in quantum mechanics,
especially in quantum systems in the presence of topological defects, which are
usually modelled by point interactions. In general, it is possible to apply
some kind of regularization procedure, as the vanishing of the wave function at
the location of the singularity, ensuring that the wave function is
square-integrable and then can be associated with a physical state. However, a
study based on the self-adjoint extension approach can lead to more general
boundary conditions that still gives acceptable physical states. We exemplify
the methods by exploring the bound and scattering scenarios of a spin 1/2
charged particle with an anomalous magnetic moment in the Aharonov-Bohm
potential in the conical space.
