Chapter 6: Correlation Functions and Spectra
In the Fourier Grid Hamiltonian (FGII) method (Marston, 1989) the coordinates x, x' are discretized at N evenly spaced points:
and thus, the Hamiltonian is an N x N matrix with 
corresponding to position 
The potential energy matrix elements are given by the prescription that the off-diagonal elements vanish and that the diagonal elements are given by the local evaluation of V(x):
The kinetic energy matrix elements are given (for N even) by:
Adding the kinetic and potential energies we obtain:
corresponding to position
The potential energy matrix elements are given by the prescription that the off-diagonal elements vanish and that the diagonal elements are given by the local evaluation of V(x):