Reflectionless Quantum Wire

When a quantum wire is not straight, an effective potential appears in the Schrödinger equation according to its curvature. Generally due to this geometrical potential the electron along the wire cannot change its direction of the motion without reflection. Here, the new curve is proposed in which the electron traverses changing its direction without reflection. The curve is determined under the condition that the effective potential should be reflectionless one which is well-known in the scattered problem.