Barrier in front of a wall

A particle with a Gaussian wave packet hits the obstacle in front of an impenetrable wall. Only a small part of the wave packet tunnels through the barrier. This time the energy of the incoming wave packet matches the energy of a resonant state. This results in a significant excitation behind the barrier. The resonance has a rather long lifetime. The particle can be found behind the barrier with significant probability, even after the major part of the wave packet has already left the scene.