The time-dependent Schrödinger equation: Application of absorbing boundary conditions

In this work the time-dependent Schrödinger equation, which is solved by employing absorbing boundary conditions, is considered. To achieve this, a negative imaginary short-range potential was added to the potential at the asymptotic regions. The study concentrated on deriving the necessary conditions for the absorbing potential to be almost perfect. The theoretical findings are supported by a numerical study carried out for a one-dimensional (reactive) model.