# Problem 6 By considering the commutator, show that the following Hermitian matrices may be|simultaneously diagonalized. Find the eigenvectors common to both and verify that under a unitarytransformation to this basis, both matricies arediagonalized21 0 111(4)0 0 01-121 0 1-1Since is degenerate and A is not, you must be prudent in deciding which matrix dictates the choiceof basis

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Asked Sep 26, 2019
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It's a problem in the field of quantum mechanics.

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## Expert Answer

Step 1

For simultaneous diagonalization of the matrix, the matrices specified by Ω and Λ must commute,

For the matrices to commute, their commutator brackets must evaluate to zero,

Step 2

Evaluating the commutator bracket, we have

Step 3

The commutator for Ω and Λ equals zero which proves that it is simultaneously diagonalizable

To calculate the eigenvectors of Ω, first calculate the eigenvalues of the Ω by using the  characteristic equation

Ω-...

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