Asymptotic boundary conditions of one-dimensional atomic model in intense laser field are derived using Fourier transformation.Errors of the three asymptotic boundary conditions are analyzed.The probability distribution and the average energy for one-dimensional hydrogen atom in the intense laser field are numerically computed using the first boundary condition and the symplectic method for the linear inhomogeneous canonical equations.The results are compared with theoretic analyses.

In a quantum system,when the Hamiltonian operator is time-dependent,"artificial" variables are introduced to construct the symplectic integrators with arbitrary high order accuracy.As an example,the time-evolution of an electron in the infinite deep potential well interacting with an animated laser field is investigated.The computed results coincide with the theory and can preserve the norm,which show that the methods are reasonable.

For an intense field model, the time-dependent Schrødinger equation with initial and boundary conditions can be discretized into the inhomogeneous linear canonical equation by substituting the symmetric difference quotient for the partial derivative. As the general solution of its homogeneous equation and the particular solution of the inhomogeneous equation can be generalized by the symplectic transformation, it is a reasonable numerical method to use the symplectic scheme. To prove its utility, a simple example is described using the symplectic scheme and RK method, and compared with the exact solution. The results show that the solution using the symplectic scheme can preserve the intrinsic properties of the equations after a long evolution, but RK method cannot.

A charge conservation statistics enhancement method used in semiconductor divice Monte Carlo simulation is approached,which smoothes the charge fluctuation caused by the statistics enhancement, and keeps the continuation of cross edge charge flow. As an example, Schottky barrier diode characteristics is simulated using this method.

The symplectic algorithm in the complex symplectic space is the algorithm that preserves the Wronskian.The Wronskian calculated by using the symplectic scheme keeps unchanged which is in good agreement with theoretical analyses after a long distance of computation.The numerical solutions of the one dimensional model of strong laser field are calculated by using the Wronskian preserving and symplectic scheme.