We present one another consideration of the propagator for a quantum particle in the presence of the step potential. This problem has been under treatment several times both as quantum and as stochastic ones but the explicit formulas derived in [12] for a problem in the "imaginary time representation" could hardly be used for computations in quantum case. Following mainly [5] the systematic exploration performed and the explicit expressions for the propagator in real time are constructed.
We have considered a one-dimensional Krönig-Penney like model of coherent electron transport. The model represents a curved channel with disordered scattering centers, which is subjected to an external uniform electric field. We have shown that the transmission coefficient of the channel is exponentially sensitive to both transverse and longitudinal field magnitudes.
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