Parametrization of complex absorbing potentials for time-dependent quantum dynamics using multi-step potentials

Abstract

In this work, the reflection and transmission of plane waves are examined from a ‘true’ complex potential. In our previous paper a simple and exact numerical procedure was proposed for treating the absorbing potential problem. The comparison of this multi-step potential method with the time-dependent wavepacket approach gave very good agreement, so our present aim is to examine an appropriate polynomial form of negative complex potentials (NCPs) using the step potential method. Calculations have been presented that optimize the coefficients and exponents of the power functions so as to get a minimal value for the sum of the reflection and transmission coefficients as a function of the kinetic energy and the absorbing length.