| 11. | This argument also gives an algorithm for finding the Hamiltonian path.
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| 12. | The modified eigenstates can be found by diagonalising the modified Hamiltonian.
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| 13. | These effects are more prominent if the original Hamiltonian had degeneracy.
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| 14. | Where and have the same eigenvalues and is a free Hamiltonian.
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| 15. | Justice Story, in his Commentaries, espouses the Hamiltonian position.
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| 16. | Thus, the matrix exponential of a Hamiltonian matrix is symplectic.
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| 17. | Has to be added to the above non-relativistic Hamiltonian.
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| 18. | An example is the magnetic dipole term in the hyperfine Hamiltonian,
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| 19. | The undamped Duffing equation is known to be a Hamiltonian system:
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| 20. | :: They also show up in Hamiltonian mechanics as well.
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