Design of quantum filters with pre-determined reflection and transmission properties

A method based on the solution of the one-dimensional single channel inverse scattering is proposed for the design of quantum filters having specific reflection and transmission properties. The inversion procedure allows one, via modifications of a prefabricated prototype system, to reach the desired filter properties. The feasibility of the method is demonstrated on several examples, where filter properties are requested in different energy ranges. The shape and range of the corresponding potential are smooth and therefore they render themselves to applications in microelectronics, nanostractures and in quantum devices.