A quantum waveguide with Aharonov–Bohm magnetic field

In a previous study, we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disk window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We proved that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. In the present work, we study the effect of the presence of a magnetic field of Aharonov–Bohm type on this system. Precisely, we prove that in the presence of such field, there is some critical values of a₀>0, for which we have absence of the discrete spectrum for . We give a sufficient condition for the existence of discrete eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd.