Electron multichannel scattering by narrows of quantum waveguides

Recent years show sharp increase of interest in the study of devices based on electron transport in nanowires. Such devices can be used as field effect transistors, resonant tunneling diodes, lasers, as well as qubits. Quantum resonators in nanowires (quantum waveguides) can be created by application of an external potential to certain areas of the waveguide. However, there is a much easier way to create quantum resonators: by forming two or more narrows in the waveguide. To analyze the effect of the narrows in the quantum waveguide on electron transport let us first briefly consider the distribution of electron wave of arbitrary energy in an undeformed waveguide.