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Abstract: We study the time-dependent scattering of a quantum mechanical wave packet ata barrier for energies larger than the barrier height, in the semi-classicalregime. More precisely, we are interested in the leading order of theexponentially small scattered part of the wave packet in the semiclassicalparameter when the energy density of the incident wave is sharply peaked aroundsome value. We prove that this reflected part has, to leading order, a Gaussianshape centered on the classical trajectory for all times soon after its birthtime. We give explicit formulas and rigorous error bounds for the reflectedwave for all of these times.



Author: Volker Betz, Alain Joye, Stefan Teufel

Source: https://arxiv.org/







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