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Spin wave function of a spin ${1\over 2}$ particle is given to be $$ \vert\phi\rangle = \left( \begin{array}{r} \displaystyle {3\over5} \\ \displaystyle -{4\over 5} \end{array} \right) $$
- Find the ratio of probabilities that $S_z$ has values $\pm\hbar/2$.
- Find the ratio of probabilities that $S_x$ has values $\pm\hbar/2$.
- Compute the average value of spin projection along the direction (1,1,1).
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