Pseudospectral method for solving the time-dependent Schrödinger equation in spherical coordinates

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Abstract
In this paper we describe a numerically efficient pseudospectral method for solving the time‐dependent Schrödinger equation in spherical coordinates. In this method the translational kinetic energy operator is evaluated with a Fourier transform. The angular dependence of the wave function is expanded on a two‐dimensional grid in coordinate space and the angular part of the Laplacian is evaluated by a Gauss–Legendre–Fourier transform between the coordinate and conjugate angular momentum representations. The potential energy operator is diagonal. Calculations performed for a model system representing H2 scattering from a static corrugated surface yield transition probabilities identical to those obtained with the close coupled wave packet (CCWP) method. The new algorithm will be more efficient than the CCWP method for problems in which a large number of rotational states are coupled.