Optimal reflection-free complex absorbing potentials for quantum   propagation of wave packets
  The conditions for optimal reflection-free complex-absorbing potentials (CAPs) are discussed. It is shown that the CAPs as derived from the smooth-exterior-scaling transformation of the Hamiltonian,[J. Phys. B. 31, 1431 (1998)], serve as optimal reflection-free CAPs (RF-CAPs) in wave-packet propagation calculations of open systems. The initial wave packet, can be located in the interaction region (as in half collision experiments) where the CAPs have vanished or in the asymptote where the absorbing potential non zero. As we show the optimal CAPs can be introduced also in the region where the physical potential has not vanished. The un-avoided reflections due to the use of finite number of grid points (or basis functions) are discussed. A simple way to reduce the "edge grid" reflection effect is described. 
Oded Shemer, Daria Brisker, and Nimrod Moiseyev