Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrödinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.