A beam of spin-1 particles is prepared in the state
\[\left|{\psi}\right\rangle
=\frac{2}{\sqrt{29}}\left|{1}\right\rangle +i\frac{3}{\sqrt{29}}\left|{0}\right\rangle -\frac{4}{\sqrt{29}}\left|{-1}\right\rangle .\]

What are the possible results of a measurement of the spin component \(S_z\), and with what probabilities would they occur?

What are the possible results of a measurement of the spin component \(S_x\), and with what probabilities would they occur?

Plot histograms of the predicted measurement results from parts (a) and (b), and calculate the expectation values for both measurements.