Quantum Reflection Times for Attractive Potential Tails

The time gain experienced by the quantum reflection process was analyzed. Such a time gain (delay) represented an apparent plane of reflection which is shifted in front of (behind) the surface, in a quantum reflection of an atomic beam by a surface. It was shown that the quantum reflected wave is always delayed with respect to the classical particle accelerated in the attractive potential. The results show that the quantum reflected wave experiences a time gain with respect to the free particle reflected at r = 0, except for α = 3 and k₀β₃ less than about 0.15 where it is delayed.