Recently, with the development of the ultra-short intense laser technology, we found some new phenomena such as high order harmonic generation (HHG). The research of HHG on the theory and the experiment has obtained some delightful results, and the HHG has become the very interesting and excited topics in the basic theory research.The paper describes simply the time dependent Schr?dinger equation (TDSE) under the length gauges and electric-dipole approximation by the coulomb gauges and discusses principally the method of solving the TDSE of the interaction of the laser with the module atom by the asymptotic boundary condition and symplectic algorithm. The values of the wave functions at the finite boundary can't be simply taken as zero. The boundary truncate in the numerical calculation has to be considered since the numerical calculation can not to infinite space. The ABC is implied to solve the...
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