Aharonov-Bohm effect on the bound states of an electron inside an annular cylindrical box

We solve the Schroedinger equation for an electron inside an annular cylind rical box in two situations: i) in the absence of any fields, and ii) in th e presence of a uniform, axial magnetic induction field confined and center ed in the perforation. The Aharonov-Bohm effect on the bound states of the electron is exhibited through the analysis of the dependence of the energy eigenvalues and eigenfunctions on the enclosed magnetic flux. The results o f this study serve to illustrate the roles of the magnetic vector potential and the gauge transformations in quantum mechanics.