  In this work we discuss about the problem of an electrically charged particle
placed on the symmetry axis of an electrically charged ring in a quantum
viewpoint. This problem should be an expanded version of the usual quantum ring
and quantum corral. For this purpose, we present a detailed and pedagogical
review about a version of the quantum ring focusing in mathematical aspects. As
a new result, we calculate numerically the spectrum and wave functions related
to charged particle located on the symmetry axis of charged ring and respective
wave functions using two different ways: Numerov and perturbative method.
