A classical trajectory method is used to study a diatomic molecule(HF) interacting with chirped intense laser pulses.In the model,the motion of nuclei is described with classical Hamiltonian canonical equations.The Hamiltonian equation is solved numerically by a symplectic method,and the initial conditions are chosen by a single trajectory in the field-free case at random.The classical dissociation of HF by chirped pulses is evaluated.The dissociation probabilities with different laser intensities are discussed.Dissociation probabilities at different initial states are also investigated.The dissociation process is illustrated by classical phase trajectories and energy versus nuclei separation.

The ground state wavefunctions of dilute Bose-condensed atoms in a harmonic trap at T=0 are evaluated by a symplectic shooting method.Stability of the wavefunctions is tested,and a stable wavefunction is used as the initial input of the time-dependent Gross-Pitaevskii equation. The dynamic property of stable wavefunctions is numerically examined in two phase spaces when the harmonic potential is altered suddenly.The figures in the two phase spaces are regular even after a long time of interations.For negative nonlinear coefficients,two eigenvalues related to the same negative nonlinear coefficient are calculated,and the stability of the corresponding two wavefunctions is tested.

Classical trajectories of a diatomic molecule system (CO) in laser fields are calculated in the symplectic scheme. The calculated results are compared with that with Runge-Kutta (R-K) approach. The vibration trajectories, phase trajectories and vibration energy of a diatomic molecule CO are analysed.

The dynamic properties of nonlinear Schrödinger equations are investigated numerically by using the symplectic scheme (Euler centered scheme). The dynamic behavior of cubic nonlinear Schrödinger equations with various nonlinear parameter is studied in different phase space.And the dynamic properties of cubic-quintic nonlinear Schrödinger equations are dealt with numerically by using the symplectic scheme. The dynamic behaviors of cubic-quintic nonlinear Schrödinger equations with different cubic and quintic nonlinear parameters are discussed in the phase space.It shows that the route varies with different cubic nonlinear parameters and with the increase of the quintic nonlinear parameters.

This paper presents the symplectic scheme-matrix algorithm for solving the vibrational and vibrational-rotational energy eigenvalues of ⁷Li₂ in A¹Σ_u⁺ state, and compares the computed results with the results calculated by Ley-Koo et al.. The results show that our method is convergent and reliable, and it is a reasonable method for computing the vibrational and vibrational-rotational energy eigenvalues of diatomic molecules. Since the symplectic scheme-matrix algorithm transforms the question of the solution of the radical equation of the diatomic molecules into that of the eigenvalues of the real tridiagonal symmetric matrix, it is more simple and needs smaller computer memory and less computing time compared with the method of expanding eigenfunctions of diatomic molecules used by Ley-Koo et al.

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.

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.

It is in the middle of 70's FEM has been used to obtain numerical solutions of atom and molecule problems. Little as the research work done is, it is shown that FEM is effective for one and two dimensions problems. But at least now it is impossible to use to problems of atom with n (≥ 3) electrons. A method (HFFEM) combined FEM with HF method is advanced and by using HFFEM the energy of the He-like ion ground state and mean value n> is computed on DP58. Compared the energy value obtained with one measured, the error lies between 0.3% and 0.03%. The HFFEM may be extended to applied to various atom and molecule problems.