Question

Find eigenvectors of T
\[\textbf{T} = \begin{pmatrix} 1 & 1-i \\ 1+i & 0 \\ \end{pmatrix}\]
The eigenvalues are \[\lambda_{1,2}=-1,2 \in \mathbb{R}\]

Answer 1

\[\textbf{T}|\alpha \rangle=\lambda_1|\alpha\rangle =-1|\alpha\rangle\]

Answer 2

\[2\alpha_1+(1-i)\alpha_2=-\alpha_1\quad{{(i)}}\]\[(1+i)\alpha_1+\alpha_2=-\alpha_2\quad{{(ii)}}\]

Answer 3

Linear algebra?

Answer 4

well it is , . but this question is from a Quantum Mechanics text's appendix
I can find the eigenvalues, i just can't find the eigenvalues

Answer 5

well this is just a simple eigenvalue problem , no QM required