(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the following Hamiltonian.

H=[itex]\begin{pmatrix} 20 & 1 & 0 \\1 & 20 & 2 \\0 & 2 & 30 \end{pmatrix}

[/itex]

Diagonalize this matrix using perturbation theory. Obtain eigenvectors (to first order) and eigenvalues (to second order).

Ho=[itex]\begin{pmatrix} 20 & 0 & 0 \\0 & 20 & 0 \\0 & 0 & 30 \end{pmatrix}

[/itex]

H'=[itex]\begin{pmatrix} 0 & 1 & 0 \\1 & 0 & 2 \\0 & 2 & 0 \end{pmatrix}

[/itex]

2. Relevant equations

3. The attempt at a solution

In general, diagonalizing a matrix involves finding its eigenvalues and then writing the eigenvalues on the diagonal with zeros elsewhere. Despite that, I'm just not sure how to approach this question.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Diagonalizing a matrix using perturbation theory.

**Physics Forums | Science Articles, Homework Help, Discussion**