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 c...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展开更多
With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order trunca...With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.展开更多
基金This work was supported by the National Natural Science Foundation of China (10171039, 10074019)The Special Funds for Major State Basic Research Projects (G1999032804)The Young Teacher Foundation of Jilin University.
文摘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
基金supported by the NationalNatural Science Foundation of China (Grant No.10873007)supported by the Science Foundation of Jiangxi Education Bureau (Grant No.GJJ09072)the Program for Innovative Research Team of Nanchang University
文摘With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.
