Principles of Quantum Mechanics · Problem 1.8.2

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · eigenvalue-problem

Problem

Consider the matrix

\Omega = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}

(1) Is it Hermitian? (2) Find its eigenvalues and eigenvectors. (3) Verify that

U^\dagger\Omega U

is diagonal,

U

being the matrix of eigenvectors of

\Omega