I Numerical Calculation of Hamiltonian Overlaps

[thatboi]

Hi all,
I am currently reading through this paper: https://iopscience.iop.org/article/10.1088/1367-2630/10/4/045030
and would like to reproduce their results for N=5.
My roadblock is with (9), which models the classical motion of the system. Now symbolically finding the eigenstates of the matrix (4) for N=5 is too computationally taxing to make this a viable choice. It would be easy to numerically calculate the overlap on its own, but my problem is with the gradient term. How should I deal with it numerically?
Thanks.

 

[DrClaude]

It would be easy to numerically calculate the overlap on its own, but my problem is with the gradient term. How should I deal with it numerically?

It can be approximated using a finite difference method.