I am trying to reproduce the results of a TDSE two wave-packet algorithm described in "Computational Physics: Problem Solving with Python" by Landau, Paez and Bordeianu, in section 22.4 (Wave Packet–Wave Packet Scattering). The chapter references this report and this page of results.
In pretty much all my own results and in some of those provided by the author (like this), you can see a small fragment of a wave-packet being "emitted" backwards in the very beginning of the computation. (The mass of the left packet is a fraction of the right packet's.)
The interaction potential used in these pictures is of gaussian form (attractive, but short range; shouldn't affect the packets at the initial distance). The method assumes that the wave-packets initially are far enough such that the total wavefunction is a product of two gaussians.
My question is, how does one explain this emission? This doesn't seem to make much sense physically.