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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 1409-1415 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for solving the Schrödinger equation with time-dependent potentials. When applied to the Walker–Preston model of a diatomic molecule in a strong laser field, these algorithms can have fourth order error coefficients that are three orders of magnitude smaller than the Forest–Ruth algorithm using the same number of fast Fourier transforms. Compared to the second order split-operator method, some of these algorithms can achieve comparable convergent accuracy at step sizes 50 times as large. Morever, we show that these algorithms belong to a one-parameter family of algorithms, and that the parameter can be further optimized for specific applications. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 7338-7341 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We show that the method of splitting the operator eε(T+V) to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schrödinger equation. These algorithms require knowing the potential and the gradient of the potential. One fourth order algorithm only requires four fast Fourier transformations per iteration. In a one dimensional scattering problem, the fourth order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Forest–Ruth symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to sixth order also produced better converged algorithms than iterating the Forest–Ruth algorithm to sixth order or using Yoshida's sixth order algorithm A directly. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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