TY - JOUR
T1 - Recent Progress in Symplectic Algorithms for Use in Quantum Systems
JO - Communications in Computational Physics
VL - 1
SP - 1
EP - 53
PY - 2007
DA - 2007/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7894.html
KW - 
AB - <p style="text-align: justify;">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 A<sub>2</sub>B, Hydrogen ion
H<sub>2</sub><sup>+</sup>&nbsp;and elementary atmospheric reaction N(<sup>4</sup>S)+O<sub>2</sub>(X<sup>3</sup>Σ<sub>8</sub><sup>−</sup>)→NO(X<sup>2</sup>Π)+O(<sup>3</sup>P) calculated
by means of Runge-Kutta methods and symplectic methods; the classical dissociation
of the HF molecule and classical dynamics of H<sub>2</sub><sup>+</sup>&nbsp;in an intense laser field; the
symplectic form and symplectic-scheme shooting method for the time-independent
Schrödinger equation; the computation of continuum eigenfunction of the Schrödinger
equation; asymptotic boundary conditions for solving the time-dependent Schrödinger
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.<br/></p>