Polynomial scheme for time evolution of open and closed quantum systems
  Based on the generation function of Laguerre polynomials, We proposed a new Laguerre polynomial expansion scheme in the calculation of evolution of time dependent Schr\"odinger equation. Theoretical analysis and numerical test show that the method is equally as good as Chebyshev polynomial expansion method in efficiency and accuracy, with extra merits that no scaling to Hamiltonian is needed and wider suitability. 
Jun Jing and H.R. Ma