The Gauss Wave Packets Scattering on the Regular Lattice of Finite Length

In this work we have studied in detail the one-dimensional scattering on the lattice formed by the row of N identical delta-barriers which is the one-dimension diffraction grating for electrons. The steady-state wave functions psi(E,x) and scattering amplitudes were found by the transfer-matrix method. The transmission factor T = T(E) spectrum consists of the alternating transparency and opacity zones. Inside of the transparency zones T(E) is modulated proportionally to the Chebyshev polynomial of the second kind so that there are N - 1 narrow spectral lines of full transmittivity in each zone. The amplitude of modulation increases considerably near the edges of zones where there are a few narrow spectral lines of full opacity too. In this lines of full opacity the steady-state wave functions have large resonant amplitudes inside the lattice.