A numerically exact spectral method for solving the timehyphen;dependent Schrouml;dinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a twohyphen;dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the closehyphen;coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.
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