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A numerical-analytical simulation of scattering by a three-barrierheterostructure of an electronic Gaussian wave packet, the spectral width ofwhich is on the order of the distance between the levels of the doublet ofquasi-stationary states, is carried out. It is shown that as a result ofscattering, damped waves of electron charge and current densities are formedoutside the double well, their characteristics are determined by the structureof the initial wave packet and the poles of the scattering amplitudes. Thefrequency of these waves is equal to the difference frequency of the doublet,the wavenumber is the difference between the wave numbers of free motion ofelectrons with resonant energies, and the speed of their propagation is theratio of these quantities. The system can go into the regime of repetition oramplification of the emission of electron waves if a periodic resonant pumpingof the doublet population is provided by scattering of a series of coherentwave packets.

Formation of probability density waves and probability current density  waves by excitation and decay of a doublet of quasistationary states of a  three-barrier heterostructure upon scattering of gaussian wave packets