Quantum Fundamentals 2022
The operator \(\hat{S}_x\) for spin-1 particles, can be written in matrix form in the \(S_z\) basis as:
\[\hat{S}_x=\frac{\hbar}{\sqrt{2}}
\begin{pmatrix}
0&1&0\\ 1&0&1 \\ 0&1&0 \\
\end{pmatrix}
\]
Find the eigenvalues of this matrix.
Find the eigenvectors corresponding to each eigenvalue.