This work presents a detailed analysis of complex absorbing potentials empl
oyed to eliminate reflection or wrap-around of wave packets at numerical gr
id boundaries. In particular, a limiting value for the maximum propagation
time step is derived, beyond which the complex potential may introduce mass
ive errors and the Chebyshev propagation scheme is found to fail. PACS numb
er(s): 02.70.-c, 73.23.Ad, 73.23.Hk.