Scattering of a wave packet by the Pöschl-Teller potential well

We investigate the scattering of a wave packet by the Poschl-Teller potential in momentum representation. The scattering dynamics of the wave packet for a long-time evolution is feasible in this representation. With the wave function in momentum space, we can construct the time-dependent phase space Wigner function. The corresponding density function in coordinate space is then calculated through the Wigner function. The reflectionless wave packet for integer nu and partially reflected for non-integer nu are demonstrated by analyzing the Wigner function.