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Chin. Phys. B, 2022, Vol. 31(1): 013201    DOI: 10.1088/1674-1056/ac11d6

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

Shun Wang(王顺) and Wei-Chao Jiang(姜维超)
College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
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.
Keywords:  time-dependent Schrö      dinger equation (TDSE), smooth exterior complex scaling (SECS) absorbing method, Arnoldi propagator  
Received:  03 April 2021      Revised:  04 June 2021      Accepted manuscript online:  07 July 2021
PACS:  32.80.Fb (Photoionization of atoms and ions)  
  33.20.Xx (Spectra induced by strong-field or attosecond laser irradiation)  
  31.15.A- (Ab initio calculations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12074265 and 11804233).
Corresponding Authors:  Wei-Chao Jiang     E-mail:

Cite this article: 

Shun Wang(王顺) and Wei-Chao Jiang(姜维超) Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator 2022 Chin. Phys. B 31 013201

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