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

TL;DR

This paper introduces a new quantum scattering model on a potential step that reveals a transitional region affecting particle reflection and transmission times, providing insights into the dynamics of quantum particles.

Contribution

The model reconstructs the history of transmitted and reflected particles and predicts a transitional region with nonzero reflection probability, unlike conventional models.

Findings

Existence of a transitional spatial region behind the potential step.

Monotonous variation of transmitted particles' average velocity.

Defined dwell and asymptotic group times for subprocesses.

Abstract

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