We have computed the bound state energies 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 exists and the binding energy corresponds to the value obtained recently by
Schult, Ravenhall and Wyld. When the ratio of the two widths is varied the binding
energy changes. The variation of the energy with the ratio of the widths is obtained and shown graphically. A similar study is also completed for YTT? and "LT' shaped
geometries. It is shown that a nondegenerate bound state of the electron exists for
a range of values of the ratio of the two widths; outside the range the state
becomes degeneiate with the energy continuum.