Gradient symplectic algorithms for solving the Schrodinger equation with time-dependent potentials
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A class of fourth order algorithms called gradient symplectic algorithms, for solving Schrdinger equation with explicit time-dependent potentials were derived. These algorithms were characterized by having only positive factorization coefficients and their efficiency could be enhanced by knowing the gradient of the potential. These algorithms were applied to the Walker-Preston model of a diatomic molecule in a strong laser field. It was shown that these algorithms belong to a one-parameter family of algorithms and that these parameters could be optimized for specific applications.
