Investigation on the reflection and transmission properties of complex absorbing potentials

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Abstract
The reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy. Explicit formulas are obtained which describe the reflection and transmission properties of monomial CAPs −iηxn with high accuracy. These properties are now well understood. The approximate results are compared to exact analytical results available for quadratic CAPs, and to numerical results obtained by wave packet propagation followed by an energy resolved analysis. The approximate, but accurate, description of the action of the CAP is finally used to determine optimal CAP parameters. CAP length, strength, and order can now be chosen in such a way that the sum of reflection and transmission is minimized. Optimal parameters are compiled for different energies and energy intervals.