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Based on the generation function of Laguerre polynomials, We proposed a newLaguerre polynomial expansion scheme in the calculation of evolution of timedependent Schr\"odinger equation. Theoretical analysis and numerical test showthat the method is equally as good as Chebyshev polynomial expansion method inefficiency and accuracy, with extra merits that no scaling to Hamiltonian isneeded and wider suitability.Comment: 19 pages, 6 figures, Phys.Rev.E (accepted

Polynomial scheme for time evolution of open and closed quantum systems