Bound quantum states in crossed-wire systems

Abstract

The author has calculated the ground-state energy of an electron which is trapped at the intersection of a cross formed by two quantum wires. The widths of the wires forming the cross are assumed to vary independently. When the widths are equal, a bound state with energy below the energy continuum exists. The energy corresponds to the value obtained by Schult et al. (1988). When the ratio of the two widths is varied, the energy changes. The variation in the energy with the ratio of the widths is obtained and is shown graphically. It is observed that the energy decreases as one of the widths is allowed to increase. Numerical calculation indicates that the binding energy approaches zero asymptotically and the bound electronic state merges with the energy continuum. The author also calculated the energy of an electron trapped by a double cross. There are two bound states of the electron corresponding to symmetric and antisymmetric configurations. The energy of these states is calculated numerically. The possibility that the electron oscillates between the centres of the double cross is discussed and the frequency of oscillations is estimated.