Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract

We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling (SECS) absorbing method and Arnoldi propagation method. Such combination has not been reported in the literature. The proposed scheme is particularly useful in the applications involving long-time wave propagation. The SECS is a wonderful absorber, but its application results in a non-Hermitian Hamiltonian, invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian. We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian. The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet (XUV) and strong infrared (IR) laser pulses. Both perfect absorption and stable propagation are observed.