Recent Progress in Symplectic Algorithms for Use in Quantum Systems (Communications in Computational Physics, 2007)
In this paper we survey recent progress in symplectic algorithms for use inquantum systems in the following topics: Symplectic schemes for solving Hamiltoniansystems; Classical trajectories of diatomic systems, model molecule A2B, Hydrogen ionH2+ and elementary atmospheric reaction N(4S)+O2(X3Σ8−)→NO(X2Π)+O(3P) calculatedby means of Runge-Kutta methods and symplectic methods; the classical dissociationof the HF molecule and classical dynamics of H2+ in an intense laser field; thesymplectic form and symplectic-scheme shooting method for the time-independentSchrödinger equation; the computation of continuum eigenfunction of the Schrödingerequation; asymptotic boundary conditions for solving the time-dependent Schrödingerequation of an atom in an intense laser field; symplectic discretization based on asymptoticboundary condition and the numerical eigenfunction expansion; and applicationsin computing multi-photon ionization, above-threshold ionization, Rabbi oscillationand high-order harmonic generation of laser-atom interaction.