Tunneling of wave packages through resonant quantum systems

Tunneling of wave packages through resonant quantum systems presented in an S-matrix form is investigated. An arbitrary incident wave package can be written as the superposition of the Gaussian-form pulses and for latter ones the exact analytic solution was obtained already. As a practically interesting case, the transition of the rectangular wave package through the one-resonant level system is considered. Using developed recently modified saddle-points method the time-delay (Δt) of the wave pulses having Gaussian and rectangular form transmitted through a quantum system with resonance level is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependency Δt from width and energy of resonance levels, and the momentum of incident wave-package are illustrated. The results are compared with the ones obtained for tunneling of the one Gaussian package. Possible applications are discussed.