Fourier second-order differencing fast

Equation (3.12) is then solved without further approximation and within a model including all multiphoton processes. The solution of (3.8) is obtained by the second-order differencing fast Fourier transform (SOD-FFT) method [287, 288, 299]. The relevant PESs for the multiphoton ionization process considered here are the X, A, b, (2) 77g, and ion states. The PESs and the transition dipole moments are obtained from ab-initio data (Sect. 3.1.5 and [328]). 

A very simple procedure for time evolving the wavepacket is the second order differencing method. Here we illustrate how this method is used in conjunction with a fast Fourier transfonn method for evaluating the spatial coordinate derivatives in the Hamiltonian. 

The basic technique used to propagate the wave packet in the spatial domain is the fast Fourier transform method [287, 288, 299, 300]. The time-dependent Schrodinger equation is solved numerically, employing the second-order differencing approach [299, 301]. In this approach the wave function Sit t = t St is constructed recursively from the wave functions at t and t" = t — St. The operator including the potential energy is applied in phase space and that of the kinetic energy in momentum space. Therefore, for each... 

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