# 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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4. ### Calculating eigenvectors/values from Hamiltonian

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10. ### Perturbed Hamiltonian Matrix for Quantum Harmonic Oscillator

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13. ### How Potts model hamiltonian is equal to hamiltonian matrix

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14. ### Hamiltonian matrix off diagonal elements?

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15. ### Hamiltonian matrix and eigenvalues

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16. ### Feynman clock's Hamiltonian matrix reduction

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17. ### Tight binding hamiltonian matrix

Can somebody explain to me why, when we work with fermions, the tight binding Hamiltonian matrix has a form 0 0 -t -t 0 0 +t +t -t +t 0 0 -t +t 0 0 the basis are |\uparrow,\downarrow>, |\downarrow,\uparrow>, |\uparrow\downarrow,0>, |0,\uparrow\downarrow>, Why there is +t and -t? (I...
18. ### Hamiltonian matrix eigenvalue calculation

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20. ### A Starting with the Schrodinger equation, how do we find the Hamiltonian matrix?

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21. ### Computing Hamiltonian matrix for a 1-D spin chain.

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24. ### Constructing Hamiltonian Matrix from Sz Basis States for Quantum Spin Chains

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25. ### How to dertermine the Hamiltonian matrix

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26. ### Hamiltonian Matrix Eq. 8.43 Explained - Feynman III Quantum Mechanics

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