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Problem/QM-06021

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A dynamical variable \(S\) of a system is represented by a \(3\times3\) matrix: \begin{eqnarray} S= \begin{pmatrix} 0 & 1 & 0\\ 1 & 0 & 1\\ 0&1&0 \end{pmatrix}. \end{eqnarray} 

  1. Find all allowed values of \(S\). If the state of a system is given by the vector \[ f= \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} \]
  2. Compute the probability of getting possible different values when a measurement of \(S\) is made.

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