What is Hamiltonian matrix: Definition and 26 Discussions

In mathematics, a Hamiltonian matrix is a 2n-by-2n matrix A such that JA is symmetric, where J is the skew-symmetric matrix




J
=


[



0



I

n








I

n




0



]




{\displaystyle J={\begin{bmatrix}0&I_{n}\\-I_{n}&0\\\end{bmatrix}}}
and In is the n-by-n identity matrix. In other words, A is Hamiltonian if and only if (JA)T = JA where ()T denotes the transpose.

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  1. AzAlomar

    A Reference for empirical Tight-binding Hamiltonian of spds* vs sps*

    Is there a clear reference article/note for the 20X20 Hamiltonian matrix of the spds* Zinc-Blende system similar to the sps* reference in [1] Table (A) of Vogl P, Hjalmarson HP, Dow JD. A Semi-empirical tight-binding theory of the electronic structure of semiconductors†. J Phys Chem Solids...
  2. M

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  3. CharlieCW

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  4. F

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  5. DeathbyGreen

    Mathematica Eigenvectors 4x4 Matrix in Mathematica

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  6. DeathbyGreen

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  7. U

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  8. P

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  9. Konte

    I Hamiltonian matrix - Eigenvectors

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  10. L

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  11. M

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  12. N

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  13. B

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  14. T

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  15. Roodles01

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  16. S

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  17. G

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  18. N

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  19. R

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  20. L

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  21. M

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  22. W

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  23. R

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  24. L

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  25. H

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  26. M

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