Polynomial scheme for time evolution of open and closed quantum systems

Based on the generating function of Laguerre polynomials, we propose a Laguerre polynomial expansion scheme in the calculation of the evolution of the time-dependent Schrodinger equation. Theoretical analysis and numerical tests show that the method is equally as good as the Chebyshev polynomial expansion method in efficiency and accuracy, with the additional merits that no scaling to the Hamiltonian is needed and it has wider suitability.