Fourier grid Hamiltonian method

Balint-Kurti G G, Dixon R N and Marston C C 1990 The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions J. Chem. See. Faraday Trans. 86 1741... 

Chu S I 1991 Complex quasivibrational energy formalism for intense-field multiphoton and above-threshold dissociation—complex-scaling Fourier-grid Hamiltonian method J. Chem. Phys. 94 7901... 

Adhikari, S., P. Dutta, and S. P. Bhattacharyya. 1992. A time-dependent Fourier grid Hamiltonian method formulation and application to the multiphoton dissociation of a diatomic molecule in intense laser field. Chemical Physics Letters 199 574. 

Balint-Kurti, G. G., and C. L. Ward. 1991. Two computer programs for solving the Schrddinger equation for bound-state eigenvalues and eigenfunctions using the Fourier grid Hamiltonian method. Computer Physics Communications 67 285. 

Normally the TDSE cannot be solved analytically and must be obtained numerically. In the numerical approach we need a method to render the wave function. In time-dependent quantum molecular reaction dynamics, the wave function is often represented using a discrete variable representation (DVR) [88-91] or Fourier Grid Hamiltonian (FGH) [92,93] method. A Fast Fourier Transform (FFT) can be used to evaluate the action of the kinetic energy operator on the wave function. Assuming the Hamiltonian is time independent, the solution of the TDSE may be written... 

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