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We present a new model of scattering a quantum particle on the potentialstep, which reconstructs the prehistory of the subensembles of transmitted andreflected particles by their final states. Unlike the conventional one thismodel predicts the existence of a transitional spatial region behind thepotential step where the probability to find reflected particles is nonzero andthe average velocity of transmitted particles monotonously varies betweenasymptotic values. For both subprocesses we define the dwell and asymptoticgroup times.

Scattering a quantum particle on the potential step: Characteristic times for transmission and reflection