We discuss a solution of the time-dependent Schrödinger equation that incorporates absorbing boundary conditions and a method for extracting the reflection and transmission probabilities for wave packets interacting with time-dependent potential barriers. We apply the method to a rectangular barrier that moves with constant velocity, an oscillating rectangular barrier, a locally periodic barrier with an amplitude modulated by a traveling wave, and a locally periodic potential with an amplitude modulated by a standing wave. Visualizations of the reflection phenomena are presented with an emphasis on understanding these systems from their dynamics. Applications to non-stationary neutron optics experiments are discussed briefly.
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February 01 2014
Wave packet scattering from time-varying potential barriers in one dimension
Robert M. Dimeo; Wave packet scattering from time-varying potential barriers in one dimension. Am. J. Phys. 1 February 2014; 82 (2): 142–152. https://doi.org/10.1119/1.4833557
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