Tunneling of rectangular 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 a one-resonant level system is considered. Using developed recently modified saddle-points method the transition of the wave package having a Gaussian and a rectangular form is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependence of tunneling time on the 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.