Numerical Calculation of Hamiltonian Overlaps

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SUMMARY

The discussion centers on the numerical calculation of Hamiltonian overlaps for a system with N=5, referencing a specific paper from the Journal of Physics. The primary challenge is the computational difficulty in symbolically finding the eigenstates of the matrix presented in equation (4). Participants suggest using a finite difference method to approximate the gradient term, which is essential for overcoming the computational roadblock in reproducing the results.

PREREQUISITES
  • Understanding of Hamiltonian mechanics
  • Familiarity with eigenstate calculations
  • Knowledge of numerical methods, specifically finite difference methods
  • Basic proficiency in computational physics or numerical simulations
NEXT STEPS
  • Research finite difference methods for numerical differentiation
  • Explore computational techniques for eigenstate calculations in quantum systems
  • Study the specific Hamiltonian model discussed in the referenced paper
  • Investigate numerical libraries or software that facilitate Hamiltonian simulations
USEFUL FOR

Researchers in computational physics, quantum mechanics students, and anyone involved in numerical simulations of Hamiltonian systems will benefit from this discussion.

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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