The symplectic scheme-shooting method （SSSM） for solving the two-dimensional time-independent Schrodinger equation is presented. The generalized time-independent Schrodinger equation based on the active and cyclic coordinates is evaluated. The procedure of the separation of the active and cyclic coordinates of A2B type molecule （C2v symmetry） is given
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.
