中国物理B ›› 2007, Vol. 16 ›› Issue (7): 1822-1826.doi: 10.1088/1009-1963/16/7/002

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Pseudospectral method with symplectic algorithm for the solution of time-dependent Schr?dinger equations

乔豪学1, 史庭云2, 卞学滨3   

  1. (1)Department of Physics, Wuhan University, Wuhan 430072, China; (2)State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China; (3)State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;Graduate School of the Chinese Academy of Sciences, Beijing 100049, China
  • 收稿日期:2006-11-08 修回日期:2006-11-30 出版日期:2007-07-20 发布日期:2007-07-04

Pseudospectral method with symplectic algorithm for the solution of time-dependent Schrödinger equations

Bian Xue-Bin(卞学滨)a)c), Qiao Hao-Xue(乔豪学)b), and Shi Ting-Yun(史庭云)a†   

  1. a State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China; b Department of Physics, Wuhan University, Wuhan 430072, China; c Graduate School of the Chinese Academy of Sciences, Beijing 100049, China
  • Received:2006-11-08 Revised:2006-11-30 Online:2007-07-20 Published:2007-07-04

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摘要： A pseudospectral method with symplectic algorithm for the solution of time-dependent Schr\"{o}dinger equations (TDSE) is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.

关键词: pseudospectral method, symplectic algorithm, high-order harmonic generation

Abstract: A pseudospectral method with symplectic algorithm for the solution of time-dependent Schr?dinger equations (TDSE) is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.

Key words: pseudospectral method, symplectic algorithm, high-order harmonic generation

中图分类号:  (Photoionization and excitation)

  • 32.80.-t
31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)