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

Question

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

unklerhaukus · Answer

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

unklerhaukus · Answer

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

anonymous · Answer

Linear algebra?

unklerhaukus · Answer

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

unklerhaukus · Answer

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