Wednesday, September 30, 2015

A very useful formula: diagonalisation of 2 x 2 matrix

It is amazing to me how much theoretical physics and chemistry ends with diagonalising a 2 x 2 Hermitian matrix!
e.g. from Marcus-Hush theory of electron transfer to the BCS theory of superconductivity...

Yet I find I am often scrambling to get the algebra right. Finally, I have written down the eigenvalues and eigenvectors in a form that I find the most useful. I give them below (partly so I won't have to keep finding them...). The version below is actually taken from this paper


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1 comment:

  1. Ben PowellJune 10, 2019 at 2:14 PM

    The above assumes that H_12 = H_21, which implies that both are real (assuming the Hamiltonian is Hermitian). It would be useful to also have the results for the complex case H_12^* - H_21 to hand

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