Find the eigenvalues of the following matrix: 0 € 0 € 1 € H = (3) 0 € 0 where e > 0 is a positive, real constant. Matrices of this form show up a lot when doing perturbation theory in quantum...

Extracted text: Find the eigenvalues of the following matrix: 0 € 0 € 1 € H = (3) 0 € 0 where e > 0 is a positive, real constant. Matrices of this form show up a lot when doing perturbation theory in quantum mechanics. Then expand each eigenvalue in a Taylor series to second order in e, assuming e « 1. This means that it can have a term independent of e, and/or a term linear in e, and/or a term quadratic in e, but you're leaving out terms of order e', e“, etc. Note that I asked you for the eigenvalues but I did not ask for the eigenvectors.