Delay time in a single barrier for a movable quantum shutter

The transient solution and delay time for a δ potential scatterer with a movable quantum shutter is calculated by solving analytically the time-dependent Schroedinger equation. The delay time is analyzed as a function of the distance between the shutter and the potential barrier and also as a function of the distance between the potential barrier and the detector. In both cases, it is found that the delay time exhibits a dynamical behavior and that it tends to a saturation value Δtsat in the limit of very short distances, which represents the maximum delay produced by the potential barrier near the interaction region. The phase time τθ, on the other hand, is not an appropriate time scale for measuring the time delay near the interaction region, except if the shutter is moved far away from the potential. The role played by the antibound state of the system on the behavior of the delay time is also discussed.