Volume 2, Issue 1
Recent Progress in Symplectic Algorithms for Use in Quantum Systems

X. S. Liu ,  Y. Y. Qi ,  J. F. He and P. Z. Ding

Commun. Comput. Phys., 2 (2007), pp. 1-53.

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  • Abstract

In this paper we survey recent progress in symplectic algorithms for use in quantum systems in the following topics: Symplectic schemes for solving Hamiltonian systems; Classical trajectories of diatomic systems, model molecule A2B, Hydrogen ion H+ 2 and elementary atmospheric reaction N( 4S)+O2(X 3Σ − g )→NO(X 2Π)+O( 3P) calculated by means of Runge-Kutta methods and symplectic methods; the classical dissociation of the HF molecule and classical dynamics of H+ 2 in an intense laser field; the symplectic form and symplectic-scheme shooting method for the time-independent Schr ¨odinger equation; the computation of continuum eigenfunction of the Schr ¨odinger equation; asymptotic boundary conditions for solving the time-dependent Schr ¨odinger equation of an atom in an intense laser field; symplectic discretization based on asymptotic boundary condition and the numerical eigenfunction expansion; and applications in computing multi-photon ionization, above-threshold ionization, Rabbi oscillation and high-order harmonic generation of laser-atom interaction.

  • History

Published online: 2007-02

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