I Numerical Calculation of Hamiltonian Overlaps

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The discussion focuses on reproducing results from a paper related to Hamiltonian overlaps for N=5. The main challenge is the computational difficulty in symbolically finding the eigenstates of the matrix involved. The user seeks advice on how to numerically handle the gradient term, which complicates the calculations. A suggested solution is to use a finite difference method to approximate the gradient term. This approach could simplify the numerical calculations needed to achieve the desired results.
thatboi
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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.
 
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thatboi said:
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.
 

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