Using a multi-step potential as an exact solution of the absorbing potential problem on the grid

In this Letter, the reflection and transmission of plane waves are examined from a `trueʹ complex potential. A simple and exact numerical procedure has been developed for treating the absorbing potential problem. Studying sample complex absorbing potentials, we could compare our exact step potential method and the grid-based time-dependent wavepacket approach. The results indicate convincingly that the step potential scheme works fast, produces accurate numbers and performs in good agreement with the grid-based wavepacket method.