Multichannel scattering amplitudes of microparticle in a quantum wire with three-dimensional δ-potentials

Abstract

The penetration of the microparticle (electron) through the δ-potential barriers which are embedded into the quantum wire of cylindrical shape with the characteristic effect of dimensional quantization in the transverse direction is considered. The analytical expressions for the amplitudes of the multichannel scattering, which are valid for the barriers consisting of one and two δ-potentials located at some distance from each other are obtained. It is shown that the multichannel scattering turns into the one-dimensional, if the initial energy of the longitudinal motion of electron is not sufficient to excite the higher channels of scattering. In this case, the obtained formulas for the scattering amplitudes coincide with the well-known expressions for the one-dimensional scattering. The obtained solutions satisfy the conservation law of the number of particles, which is the indirect proof of the validity of derived formulas.