In this paper, bound states energies and corresponding wave functions of H-shaped quantum wires are calculated numerically in the presence of the external magnetic and electric ¯elds. This analysis was done within the Landau gauge. With a suitable de¯nition of the external con¯nement potential, we present a numerical algorithm to calculate the pro¯le of the probability distribution of charge carriers. Our analysis shows that in the presence of the external electric and magnetic ¯elds, bound state properties of the carriers are sensitive functions of an asymmetric parameter a = Wx=Wy which measures the relative width of the quantum well in two directions. We also study many-body e®ect of the bandgap renormalization in this quasi-one-dimensional system within the dynamical random phase approximation in its leading order.
