Negative time delay for wave reflection from a one-dimensional   semi-harmonic well
  It is reported that the phase time of particles which are reflected by a one-dimensional semi-harmonic well includes a time delay term which is negative for definite intervals of the incoming energy. In this interval, the absolute value of the negative time delay becomes larger as the incident energy becomes smaller. The model is a rectangular well with zero potential energy at its right and a harmonic-like interaction at its left. 
Oscar Rosas-Ortiz, Sara Cruz y Cruz and Nicolas Fernandez-Garcia
quant-ph math-ph math.MP