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Graphene has a 4x4 Pauli matix due to a special property of graphene known as psuedospin, due to the fact that there is a "chirality" associated with the K points of the brillion zone in momentum space, that results from its unusual linear energy dispersion at the Fermi point. This is related to geometric Berrry phase. I don't know if this helps you?
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What are Hamiltonian equations?
Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.
How do find matrix inverse of 4cross 4matrix?
Next to your 4x4 matrix, place the 4x4 identity matrix on the right and adjoined to the one you want to invert. Now you can use row operations and change your original matrix on the left to a 4x4 identity matrix. Each time you do a row operation, make sure you do the same thing to the rows of the original identity matrix. You end up with the identity now on the left and the inverse on the right. You can also calculate the inverse using the adjoint. The adjoint matrix is computed by taking the transpose of a matrix where each element is cofactor of the corresponding element in the original matrix. You find the cofactor t of the matrix created by taking the original matrix and removing the row and column for the element you are calculating the cofactor of. The signs of the cofactors alternate, just as when computing the determinant
What is Hamiltonian function?
The total energy of the system simply described in classical mechanics called as Hamiltonian.
Under what conditions is it not possible to find the inverse of a matrix?
in partial report experiment, you are shown a 4x4 matrix of letters and are cued to report the letters from the first row. Assuming you recalled three of the four letters in the cued row, how many of the letters in the matrix were available in your sensory memory at the offset of the letter matrix?
Is momentum hamiltonian operator is hermitian operator?
The hamiltonian operator is the observable corresponding to the total energy of the system. As with all observables it is given by a hermitian or self adjoint operator. This is true whether the hamiltonian is limited to momentum or contains potential.
