Absorbing boundaries in time-dependent problems with discretized energy continua.

Abstract

We develop a general method for removing artifacts associated with the numerical solution of time-dependent Schrödinger equation (TDSE) involving a (multiple) energy continuum discretization. This method is the equivalent to absorbing boundaries in the case where the space is discretized. By removing the reflected part of the wave function (on the artificial boundaries of the system), one is able to reduce the computational cost of the calculations, with a benefit scaling as the power of the continuum multiplicity. As a demonstration, we apply our method to the TDSE of a hydrogen atom subjected to a laser pulse, the spontaneous emission of a two-level atom in free space, and the interaction of two photons with a two-level atom and a defect mode at the edge of a photonic band gap.