EFFICIENT TIME PROPAGATION FOR FINITE-DIFFERENCE REPRESENTATIONS OF THE TIME-DEPENDENT SCHRODINGER-EQUATION

The applicability of the Chebyshev time propagation algorithm for the solution of the time-dependent Schrodinger equation is investigated within the context of differencing schemes for the representation of the spatial operators. Representative numerical tests for the harmonic oscillator and Morse potentials display the utility and limitations of this combined approach. Substantial increases in time step are possible for these lower-order methods compared with other propagators commonly used in differencing schemes, but if very high accuracy is desired for these cases difference methods remain less efficient computationally than the corresponding spectral spatial representation when both methods are applicable.